A monochromatic, small amplitude, normally incident standing wave on a sloping beach is unstable to perturbation by subharmonic (half the frequency) edge waves. At equilibrium, edge wave shoreline amplitudes can exceed incident wave amplitudes. Here, the effect of incident wave randomness on subharmonic edge wave excitation is explored following a weakly nonlinear stability analysis under the assumption of narrow-band incident random waves. Edge waves respond to variations in both incident wave phase and amplitude, and the edge wave amplitudes and incident wave groups vary on similar time scales. When bottom friction is included, intermittent subharmonic edge wave excitation is predicted due to the combination of bottom friction and wave phase. Edge wave amplitude can be near zero for long times, but for short periods reaches relatively large values, similar to amplitudes with monochromatic incident waves and no friction.

}, keywords = {coastal engineering, finite-amplitude, generation, mechanics, physics, surface gravity waves}, isbn = {0022-1120}, doi = {10.1017/jfm.2019.214}, url = {Beach erosion and wave-induced flooding models are often initialized in O(10)-m depth, seaward of the surfzone, with wave conditions estimated from regional nonlinear spectral wave models [e.g., Simulating Waves Nearshore (SWAN)]. These models are computationally expensive for high-resolution, long-term regional O(100)-km hindcasts, and they limit examination of the effect of different climate scenarios on nearshore processes. Alternatively, computationally fast models with reduced linear wave physics enable long-term hindcasts at high spatial (\<100 m) resolution. Linear models, that efficiently transform complete spectral details from deep water through complex offshore bathymetry, are appropriate for low-frequency swell wave energy propagation. Here, two numerically different linear methods are compared: backward ray-tracing and stationary linear SWAN simulations. The methods yield similar transformations from deep water (seaward of offshore islands in Southern California) to the nearshore, O(10)-m depth. However, SWAN is sensitive to model spatial resolution, especially in highly sheltered regions, where with typical (1-2 km) resolution SWAN estimates of nearshore energy vary by over a factor of 2 relative to ray tracing. Alongshore radiation stress estimates from SWAN and ray tracing also differ, and in some cases the climatological means have opposite signs. Increasing the SWAN resolution to 90 m, higher than usually applied to regional models, yields the nearshore transforms most similar to ray tracing. Both accurate rays and high-resolution SWAN require significant computation time; however, ray tracing is more efficient if transforms are needed at relatively few locations (compared with every grid point), or if computer memory is limited. Though presently less user friendly than SWAN, ray tracing is not affected by numerical diffusion or limited by model domain size or spatial resolution.

}, keywords = {climate, continental-shelf, engineering, Grid systems, Meteorology \& Atmospheric Sciences, model comparison, Model errors, optimization, part i, refraction, Regional models, validation, wave model, wind waves}, isbn = {0739-0572}, doi = {10.1175/jtech-d-18-0123.1}, url = {Numerical models predicting surfzone waves and shoreline runup in field situations are often initialized with shoreward propagating (sea-swell, and infragravity) waves at an offshore boundary in 10-30 m water depth. We develop an offshore boundary condition, based on Fourier analysis of observations with co-located current and pressure sensors, that accounts for reflection and includes nonlinear phase-coupling. The performance of additional boundary conditions derived with limited or no infragravity observations are explored with the wave resolving, nonlinear model SWASH 1D. In some cases errors in the reduced boundary conditions (applied in 11 m depth) propagate shoreward, whereas in other cases errors are localized near the offshore boundary. Boundary conditions that can be implemented without infragravity observations (e.g. bound waves) do not accurately simulate infragravity waves across the surfzone, and could corrupt predictions of morphologic change. However, the bulk properties of infragravity waves in the inner surfzone and runup are predicted to be largely independent of ig offshore boundary conditions, and dominated by ig generation and dissipation.

}, keywords = {beach, bispectra, bispectral analysis, boundary conditions, energy-transfer, engineering, generation, gravity-waves, infragravity waves, numerical modeling, oscillations, radiation, run-up, transport}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2018.10.014}, url = {Widespread erosion associated with energetic waves of the strong 2015{\textendash}2016 El Ni{\~n}o on the U.S. West Coast has been reported widely. However, Southern California was often sheltered from the northerly approach direction of the offshore waves. The few large swells that reached Southern California were not synchronous with the highest tides. Although west coast-wide tidal anomalies were relatively large in 2015{\textendash}2016, in Southern California, total water levels (sum of tides, anomalies, and wave superelevation) were lower than during the 1997{\textendash}1998 Ni{\~n}o, and comparable to the 2009{\textendash}2010 Ni{\~n}o. Airborne lidar surveys spanning 300~km of Southern California coast show the beach response varied from considerable erosion to accretion. On average, the shoreline moved landward 10~m, similar to the 2009{\textendash}2010 El Ni{\~n}o. Some San Diego county beaches were narrower in the 1997{\textendash}1998 El Ni{\~n}o than in 2015{\textendash}2016, consistent with the higher erosion potential in 1997{\textendash}1998. Beach retreat exceeded 80~m at a few locations. However, 27\% of the shoreline accreted, often in pocket beaches, or near jetties. While adjacent beaches eroded, estuary mouths accreted slightly, and several estuaries remained or became closed during the study period. Only 12\% of cliffs eroded (mostly at the base), and the average cliff face retreat was markedly less than historical values. Only two cliff-top areas retreated significantly. Although some areas experienced significant change, the potential for coastal erosion and damage in Southern California was reduced compared to the 1997{\textendash}1998 El Ni{\~n}o, because of low rainfall, a northerly swell approach, and relatively limited total high-water levels.

}, doi = {10.1029/2018JF004771}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018JF004771}, author = {Young, Adam P. and Flick, Reinhard E. and Gallien, Timu W. and Giddings,Sarah N. and Guza, R. T. and Harvey, M. and Lenain, Luc and Ludka, B. C. and Melville, W. Kendall and O{\textquoteright}Reilly, W. C.} } @article {, title = {Nourishment evolution and impacts at four southern California beaches: A sand volume analysis}, journal = {Coastal Engineering}, volume = {136}, year = {2018}, note = {n/a}, month = {2018/06}, pages = {96-105}, type = {Article}, abstract = {Four southern California beaches were nourished with offshore sand placed as subaerial pads several meters thick, m wide, and spanning between 500 and 1500 m alongshore. Three nourishments constructed with coarser than native sand, placed in 2012 at Imperial, Cardiff and Solana Beaches, elevated subaerial sand volumes for several years even when exposed to the energetic winter waves of the 2015-16 El Nifio, followed by a stormy 2016-17 winter. As these relatively resilient pads were overwashed, landward tilted subaerial profiles (accretionary crowns) formed at the eroding front face of the originally flat-topped pads and pooling occurred in the backbeach. At Imperial Beach, nourishment sand helped prevent waves from directly impacting riprap fronting houses, while groundwater flooding behind the pad was observed at a location where the pad was elevated similar to 1.6 m above the street. As the nourishments retreated, alongshore oriented spits grew downdrift from the eroding face. The alongshore displacement of the subaerial center of mass of the 2012 nourishments is positively correlated with the seasonally varying S-xy (the alongshore radiation stress component). After four years, the net southward drift of the Imperial Beach nourishment contributed to the winter 2016 closure of the Tijuana River mouth and the associated hyper -polluted and anoxic estuary conditions. Nourishment impacts on sand levels on rocky reefs were not unambiguously detectable in the background of natural variability. Over several years, gains or losses in the total sand volume (integrated from the back beach to 8 m depth, over the few km alongshore survey spans) are sometimes comparable to nourishment volumes, suggesting relatively large interannual sediment fluxes across the control volume boundaries. The clearest trend in total volume is at Torrey Pines; during 16 years since the 2001 nourishment, about 300,000 m(3) of sand has been lost. If the trend continues, the thinning veneer of sand will be removed more often from the subaerial winter beach, exposing rocks and cobbles.

}, keywords = {Alongshore transport, barrier islands, beach fill, beach nourishment, engineering, erosion, evolution, florida, models, nourishment, observations, performance, predictions, profile, project, Sand budget, Sand replenishment, Sand spit, surf zones, Total sand volume estimate, usa, Wave-built crown}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2018.02.003}, url = {Runup on ocean beaches includes steady wave setup and oscillating swash, often decomposed into wind generated sea-swell (SS), and lower frequency infragravity (IG) waves. We show that the numerically fast, open-source numerical model 1D SWASH predicts accurately the bulk properties of runup observed on two natural beaches (one steep and one shallow sloped) for a range of incident wave conditions. The runup tongue shape was measured with a scanning lidar, and the waterline location was defined in both the observations and model with a 10 cm depth threshold. Runup is reasonably accurately predicted with energetic (e.g. 5 m significant height) incident waves, even though the assumption of 1D bound waves significantly overpredicts infragravity energy at the offshore boundary in 10 in depth. The model-data comparisons are limited by statistical chatter, often larger in runup than offshore because runup energy is concentrated in the relatively narrow infragravity IG band with low effective degrees of freedom.

}, keywords = {efficient, gravel beaches, long waves, numerical modeling, parameterization, propagation, setup, swash, Total shoreline water level, Wave runup}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2017.09.004}, url = {n/a

}, month = {Sep}, abstract = {A method is developed to estimate harbor seiche at Marina di Carrara, Italy, from the properties of wind-generated incident waves outside the harbor. A linear model of the spatial structure of amplified seiche modes is combined with empirical estimates of the response of each mode to variable incident wave forcing. These empirical coefficients parameterize the complex nonlinear transfer of energy from wind waves to lower frequency seiche. As at other small harbors (\<1 km2 surface area) on ocean coasts, and consistent with previous analyses at Carrara, the observed seiche is relatively energetic at several periods between about 1 and 15 min that are highly amplified theoretically, and the spatial structure of modeled and observed seiches agree as well. The longest seiche (≈15 min) mode is almost spatially uniform within the harbor and dominates with low-energy, short-period incident wind waves (measured 1 km offshore of the harbor). Increased wave energy and longer periods excite shorter period (1{\textendash}3 min) seiche modes with more complex spatial structure, including small areas of high amplification, which have led to operational issues. The energy in each of the six most energetic seiche modes is related in this paper empirically to offshore incident wind wave height and peak period, allowing detailed predictions of harbor seiche from routine wind wave forecasts. The approach appears applicable to relatively small, shallow harbors with reflective quay walls, in which the exterior harbor mouth is exposed, and the interior sheltered from energetic wind-generated waves.

}, isbn = {0733-950X}, doi = {10.1061/(asce)ww.1943-5460.0000392}, url = {Nearshore wave predictions with high resolution in space and time are needed for boating safety, to assess flood risk, and to support nearshore processes research. This study presents methods for improving regional nearshore predictions of swell-band wave energy (0.04-0.09 Hz) by assimilating local buoy observations into a linear wave propagation model with a priori guidance from global WAVEWATCH III (WW3) model predictions. Linear wave propagation, including depth-induced refraction and shoaling, and travel time lags, is modeled with self-adjoint backward ray tracing techniques. The Bayesian assimilation yields smooth, high-resolution offshore wave directional spectra that are consistent with WW3, and with offshore and local buoy observations. Case studies in the Southern California Bight (SCB) confirm that the nearshore predictions at independent (nonassimilated) buoy sites are improved by assimilation compared with predictions driven with WW3 or with a single offshore buoy. These assimilation techniques, valid in regions and frequency bands where wave energy propagation is mostly linear, use significantly less computational resources than nonlinear models and variational methods, and could be a useful component of a larger regional assimilation program. Where buoy locations have historically been selected to meet local needs, these methods can aid in the design of regional buoy arrays by quantifying the regional skill improvement for a given buoy observation and identifying both high-value and redundant observations. Assimilation techniques also identify likely forward model error in the Santa Barbara Channel, where permanent observations or model corrections are needed.

}, keywords = {buoy, directional spectra, southern california bight, swan, system}, isbn = {0739-0572}, doi = {10.1175/jtech-d-17-0003.1}, url = {A decade-long effort to estimate nearshore (20 m depth) wave conditions based on offshore buoy observations along the California coast is described. Offshore, deep water directional wave buoys are used to initialize a non stationary, linear, spectral refraction wave model. Model hindcasts of spectral parameters commonly used in nearshore process studies and engineering design are validated against nearshore buoy observations seaward of the surfzone. The buoy-driven wave model shows significant skill at most validation sites, but prediction errors for individual swell or sea events can be large. Model skill is high in north San Diego County, and low in the Santa Barbara Channel and along the southern Monterey Bay coast. Overall, the buoy-driven model hindcasts have relatively low bias and therefore are best suited for quantifying mean (e.g. monthly or annual) nearshore wave climate conditions rather than extreme or individual wave events. Model error correlation with the incident offshore wave energy, and between neighboring validation sites, may be useful in identifying sources of regional modeling errors. (C) 2016 The Authors.

}, keywords = {buoy, climate, Longshore radiation stress, models, ocean waves, refraction, spectra, storms, swell, Wave buoys, wave models, wave refraction, Wave runup}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2016.06.005}, url = {A 9 km long tracer plume was created by continuously releasing Rhodamine WT dye for 2.2 h during ebb tide within the southern edge of the main tidal channel at New River Inlet, NC on 7 May 2012, with highly obliquely incident waves and alongshore winds. Over 6 h from release, COAWST (coupled ROMS and SWAN, including wave, wind, and tidal forcing) modeled dye compares well with (aerial hyperspectral and in situ) observed dye concentration. Dye first was transported rapidly seaward along the main channel and partially advected across the ebb-tidal shoal until reaching the offshore edge of the shoal. Dye did not eject offshore in an ebb-tidal jet because the obliquely incident breaking waves retarded the inlet-mouth ebb-tidal flow and forced currents along the ebb shoal. The dye plume largely was confined to \<4 m depth. Dye was then transported downcoast in the narrow (few 100 m wide) surfzone of the beach bordering the inlet at 0.3 ms-1 driven by wave breaking. Over 6 h, the dye plume is not significantly affected by buoyancy. Observed dye mass balances close indicating all released dye is accounted for. Modeled and observed dye behaviors are qualitatively similar. The model simulates well the evolution of the dye center of mass, lateral spreading, surface area, and maximum concentration, as well as regional (inlet and ocean) dye mass balances. This indicates that the model represents well the dynamics of the ebb-tidal dye plume. Details of the dye transport pathways across the ebb shoal are modeled poorly perhaps owing to low-resolution and smoothed model bathymetry. Wave forcing effects have a large impact on the dye transport.

}, keywords = {boundary-layer, buoyant, circulation, coastal waters, currents, ebb-tidal plume, longshore, momentum balances, river plume, surf zone, system, tidal inlet, tracer transport, wave-current interaction}, isbn = {2169-9275}, doi = {10.1002/2016jc011922}, url = {Concurrent observations of waves at the base of a southern California coastal cliff and seismic cliff motion were used to explore wave-cliff interaction and test proxies for wave forcing on coastal cliffs. Time series of waves and sand levels at the cliff base were extracted from pressure sensor observations programmatically and used to compute various wave impact metrics (e.g. significant cliff base wave height). Wave-cliff interaction was controlled by tide, incident waves, and beach sand levels, and varied from low tides with no wave-cliff impacts, to high tides with continuous wave-cliff interaction. Observed cliff base wave heights differed from standard Normal and Rayleigh distributions. Cliff base wave spectra levels were elevated at sea swell and infragravity frequencies. Coastal cliff top response to wave impacts was characterized using microseismic shaking in a frequency band (20-45Hz) sensitive to wave breaking and cliff impacts. Response in the 20-45Hz band was well correlated with wave-cliff impact metrics including cliff base significant wave height and hourly maximum water depth at the cliff base (r(2) = 0.75). With site-specific calibration relating wave impacts and shaking, and acceptable anthropogenic (traffic) noise levels, cliff top seismic observations are a viable proxy for cliff base wave conditions. The methods presented here are applicable to other coastal settings and can provide coastal managers with real time coastal conditions. Copyright (C) 2016 John Wiley \& Sons, Ltd.

}, keywords = {bluff recession, california, cliff shaking, coastal cliff, erosion rates, ground motions, microseismic, model, new-zealand, ocean waves, seismic noise, shore platforms, soft rock cliffs, wave impact, wave-cliff interaction}, isbn = {0197-9337}, doi = {10.1002/esp.3928}, url = {Accurate, unbiased, high-resolution (in space and time) nearshore wave predictions are needed to drive models of beach erosion; coastal flooding; and alongshore transport of sediment, biota, and pollutants. On sheltered shorelines, wave predictions are sensitive to the directions of onshore propagating waves, and nearshore model prediction error is often dominated by directional uncertainty offshore. Here, regional wave model skill in highly sheltered Southern California is compared for different offshore boundary conditions created from offshore buoy observations and global wave model hindcasts [NOAA WaveWatch III (WW3)]. Spectral ray-tracing methods are used to transform incident offshore swell (0.04-0.09 Hz) energy at high directional resolution (1 degrees). Model skill is assessed for predictions (wave height, direction, directional spread, and alongshore radiation stress) at 16 nearshore buoy sites between 2000 and 2009. Buoy-derived boundary conditions using various estimators (maximum entropy, maximum smoothness) have similar skill and all outperform WW3-derived boundary conditions. A new method for estimating offshore boundary conditions, CMB-ADJ, combines buoy observations with WW3 predictions. Although CMB-ADJ skill is comparable to buoy-only methods, it may be more robust in varying regions and wave climatologies, and will benefit from future improvements in global wave model (GWM) predictions. A case study at Oceanside Harbor shows strong sensitivity of alongshore sediment transport estimates to the boundary condition method. However, patterns in alongshore gradients of transport (e.g., the location of model accretion and erosion zones) are similar across methods. Weak, tidally modulated coastal reflection is evident in both shallow and deep buoy observations, and significantly increases the observed directional spread.

}, keywords = {calibration, climate, coastal areas, directional spectra, pacific, part i, pitch, reanalysis, system, validation}, isbn = {0739-0572}, doi = {10.1175/jtech-d-16-0038.1}, url = {Subaerial sand levels were observed at five southern California beaches for 16 years, including notable El Ninos in 1997-98 and 2009-10. An existing, empirical shoreline equilibrium model, driven with wave conditions estimated using a regional buoy network, simulates well the seasonal changes in subaerial beach width (e.g. the cross-shore location of the MSL contour) during non-El Nino years, similar to previous results with a 5-year time series lacking an El Nino winter. The existing model correctly identifies the 1997-98 El Nino winter conditions as more erosive than 2009-10, but overestimates shoreline erosion during both El Ninos. The good skill of the existing equilibrium model in typical conditions does not necessarily extrapolate to extreme erosion on these beaches where a few meters thick sand layer often overlies more resistant layers. The modest over-prediction of the 2009-10 El Nino is reduced by gradually decreasing the model mobility of highly eroded shorelines (simulating cobbles, kelp wrack, shell hash, or other stabilizing layers). Over prediction during the more severe 1997-98 El Nino is corrected by stopping model erosion when resilient surfaces (identified with aerial imagery) are reached. The trained model provides a computationally simple (e.g. nonlinear first order differential equation) representation of the observed relationship between incident waves and shoreline change. (C) 2016 Elsevier Ltd. All rights reserved.

}, keywords = {climate, coastal, equilibrium, erosion, framework, LIDAR, littoral cell, pacific-northwest, sea-level rise, shoreline change, wave}, isbn = {0278-4343}, doi = {10.1016/j.csr.2016.05.008}, url = {Wave conditions in Southern California during the 2015-2016 El Nino were similar to the 2009-2010 El Nino, previously the most erosive (minimum beach widths and subaerial sand levels) in a 7 year record. As of February 2016, Torrey Pines Beach had eroded slightly below 2009-2010 levels, threatening the shoulder of a major highway. However, Cardiff, Solana, and Imperial Beaches, nourished with imported sand in 2012, were on average 1-2 m more elevated and more than 10 m wider than in 2009-2010. Monthly subaerial sand elevation observations showed that the nourished beaches remained consistently wider than unnourished beaches under similar wave conditions. In contrast to a 2001 nourishment at Torrey Pines built with native sized sand that was removed from the beach face during a single storm, these relatively coarse grained nourishments protected shorelines for several years, and during the significant wave attack of the 2015-2016 El Nino, as of February 2016.

}, keywords = {coastal sea-level, equilibrium, evolution, oscillation, pacific coast, profile, project, replenishment, sand engine, surf zones}, isbn = {0094-8276}, doi = {10.1002/2016gl068612}, url = {An equilibrium framework is used to describe the evolution of the cross-shore profile of five beaches (medium grain size sand) in southern California. Elevations were observed quarterly on cross-shore transects extending from the back beach to 8 m depth, for 3-10 years. Transects spaced 100 m in the alongshore direction are alongshore averaged into nineteen 700-900 m long sections. Consistent with previous observations, changes about the time average profile in many sections are captured by the first mode empirical orthogonal function (EOF). The first EOF poorly describes sections with hard substrate (less than roughly 80\% sandy bottom) and also fails near the head of a submarine canyon and adjacent to an inlet. At the 12 well-described sections, the time-varying amplitude of the first EOF, the beach state A, describes the well-known seasonal sand exchange between the shoreline and offshore (roughly between 4 and 7 m depth). We show that the beach state change rate dA/dt depends on the disequilibrium between the present state A and wave conditions, consistent with the equilibrium concepts of Wright and Short (1984) and Wright et al. (1985). Empirically determined, optimal model coefficients using the framework of Yates et al. (2009a, 2011) vary between sections, but a single set of globally optimized values performs almost as well. The model implements equilibrium concepts using ad hoc assumptions and empirical parameter values. The similarity with observed profile change at five southern California beaches supports the underlying model equilibrium hypotheses, but for unknown reasons the model fails at Duck, NC.

}, keywords = {bar, behavior, erosion, evolution, model, natural beach, north-carolina, sandbar, shoreline change, southern-california, surface-temperature, time-dependent beach}, isbn = {2169-9275}, doi = {10.1002/2015jc010893}, url = {The transformation of surface gravity waves from 11 m depth to runup was observed on the low-sloped (1/80) Agate Beach, Oregon, with a cross-shore transect of current meters, pressure sensors, and a scanning lidar. Offshore wave heights H-0 ranged from calm (0.5 m) to energetic (\> 7 m). Runup, measured with pressure sensors and a scanning lidar, increases linearly with (H0L0)(1/2), with L-0 the deep-water wavelength of the spectral peak. Runup saturation, in which runup oscillations plateau despite further increases in (H0L0)(1/2), is not observed. Infragravity wave shoaling and nonlinear energy exchanges with short waves are included in an infragravity wave energy balance. This balance closes for high-infragravity frequencies (0.025-0.04 Hz) but not lower frequencies (0.003-0.025 Hz), possibly owing to unmodeled infragravity energy losses of wave breaking and/or bottom friction. Dissipative processes limit, but do not entirely damp, increases in runup excursions in response to increased incident wave forcing.

}, keywords = {climate, dissipation, infragravity waves, intermediate, motions, nearshore, setup, Surfzone, swash oscillations, variability}, isbn = {0094-8276}, doi = {10.1002/2015gl066124}, url = {Surfzone and inner-shelf tracer dispersion are observed at an approximately alongshore-uniform beach. Fluorescent Rhodamine WT dye, released near the shoreline continuously for 6.5 h, is advected alongshore by breaking-wave- and wind-driven currents, and ejected offshore from the surfzone to the inner-shelf by transient rip currents. Novel aerial-based multispectral dye concentration images and in situ measurements of dye, waves, and currents provide tracer transport and dilution observations spanning about 350 m cross-shore and 3 km alongshore. Downstream dilution of near-shoreline dye follows power law decay with exponent -0.33, implying that a tenfold increase in alongshore distance reduces the concentration about 50\%. Coupled surfzone and inner-shelf dye mass balances close, and in 5 h, roughly half of the surfzone-released dye is transported offshore to the inner-shelf. Observed cross-shore transports are parameterized well ( r2=0.85, best fit slope 0.7) using a bulk exchange velocity and mean surfzone to inner-shelf dye concentration difference. The best fit cross-shore exchange velocity u*=1.2x10-2ms-1 is similar to a temperature-derived exchange velocity on another day with similar wave conditions. The u* magnitude and observed inner-shelf dye length scales, time scales, and vertical structure indicate the dominance of transient rip currents in surfzone to inner-shelf cross-shore exchange during moderate waves at this alongshore-uniform beach.

}, keywords = {continental-shelf, cross-shore transport, currents, driven, inner-shelf, mixing, pollution, shore, Surfzone, tracer, transport, undertow, waves, zone}, isbn = {2169-9275}, doi = {10.1002/2015jc010844}, url = {Material transport and dispersion near the mouth of a tidal inlet (New River Inlet, NC) are investigated using GPS-tracked drifters and numerical models. For ebb tide releases, velocities are largest (\> 1 ms(-1)) in two approximately 30 m wide channels that bisect the 1-3 m deep ebb shoal. In the channels, drifter and subsurface current meter velocities are similar, consistent with strong vertical mixing and 2-D hydrodynamics. Drifters were preferentially entrained in the channelized jets where drifter cluster lateral spreading rates mu(in) were small (mu(in) approximate to 0.5 m(2) s (1)). At the seaward edge of the ebb shoal, jet velocities decrease linearly with distance (to \<= 0.2 ms(-1), about 1 km from shore), and cluster spreading rates are larger with mu(out) approximate to 3 m(2) s(-1). Although the models COAWST and NearCom generally reproduce the observed trajectory directions, certain observed drifter properties are poorly modeled. For example, modeled mean drifter velocities are smaller than observed, and upon exiting the inlet, observed drifters turn north more than modeled drifters. The model simulations do reproduce qualitatively the spreading rates observed in the inner inlet, the flow deceleration, and the increase in mu(out) observed in the outer inlet. However, model spreading rates increase only to mu(out) \< 1 m(2) s(-1). Smaller modeled than observed mu(out) may result from using unstratified models. Noncoincident (in space) observations show evidence of a buoyant plume (Delta rho = 1 kg m(-3)) in the outer inlet, likely affecting drifter lateral spreading. Generally, drifter-based model performance is good within the inlet channels where tidal currents are strongest, whereas model-data differences are significant farther offshore.

}, keywords = {currents, estuary, nearshore circulation model, portugal, residence time, river plume, surf zone, system, transport, wave-current interaction}, isbn = {2169-9275}, doi = {10.1002/2014jc010541}, url = {Coastal flood riskfrom coincident high tides{\textquoteright} and energetic waves is concentrated around low-lying urban areas. Municipalities construct temporary sand berms (also known as sacrificial dunes) to manage potential flooding, however the relationships between berm geometry (e.g., height, width and length) and performance are not understood. Concomitant pressures of sea level rise and urbanization will increase active beach berming. Effective future coastal flood risk management will depend upon optimizing berm efficacy relative to geometry, placement, and water levels. Here, 34 individual berms at seven southern California locations are characterized using 18 LiDAR datasets spanning nearly a decade. Three berm classifications emerged based on deployment duration: event, seasonal and persistent. Event berms, deployed to manage specific storms or high water events, are triangular in cross-section, relatively low volume (similar to 4 m(3)/m) and low crest elevation (similar to 5 m NAVD88). Seasonal berms are larger, volumes vary from 6 to 28 m(3)/m, and average crest elevations are between 5.3 and 6.4 m. A persistent berm, captured in all LiDAR data for that area, is the largest (48 m(3)/m), longest (1.2 km), and highest mean crest elevation (7 m NAVD88) of all study berms. Total water levels, estimated using observed tides and a regional wave model coupled with an empirical runup formula, suggest that overtopping is rare. Currently, event berms are vulnerable to wave attack only a few hours per year. However, even with modest sea level rise (similar to 25 cm) or El Nino conditions, exposure increases significantly, and substantial nourishments may be required to maintain current flood protection levels. (C) 2014 Elsevier Ltd. All rights reserved.

}, keywords = {airborne lidar, Anthropogenic dune, Artificial sand dune, beach, Beach scraping, coastal defense structures, Coastal management, construction, dune erosion, Dune management, erosion, Flood, impact, LIDAR, mitigation, nourishment, perspective, prediction, Sacrificial dune, Sand embankment, scale, wave models, Winter dune}, isbn = {0964-5691}, doi = {10.1016/j.ocecoaman.2014.12.014}, url = {Cross-shore tracer exchange between the surfzone and inner-shelf is examined using temperature and dye measurements at an approximately alongshore-uniform beach. An alongshore-oriented plume is created by releasing dye continuously for 4.5 h in a surfzone alongshore current. The plume is sampled for 13 h from the release point to 700 m downstream, between the shoreline and 250 m offshore (6 m water depth). Within the surfzone (\<= 2 m depth), water is relatively warm, and dye is vertically well mixed. On the inner-shelf (3-6 m depth), alongshore currents are weak, and elevated temperature and dye co-occur in 25-50 m wide alongshore patches. Within the patches, dye is approximately depth-uniform in the warm upper 3 m where thermal stratification is weak, but decreases rapidly below 3 m with a strong thermocline. Dye and temperature vertical gradients are correlated, and dye is not observed below 18 degrees C. The observations and a model indicate that, just seaward of the surfzone, thermal stratification inhibits vertical mixing to magnitudes similar to those in the ocean interior. Similar surfzone and inner-shelf mean alongshore dye dilution rates are consistent with inner-shelf dye properties being determined by local cross-shore advection. The alongshore-patchy and warm inner-shelf dye is ejected from the surfzone by transient rip currents. Estimated Stokes drift driven cross-shore exchange is small. The transient rip current driven depth-normalized heat flux out of the surfzone has magnitude similar to those of larger-scale shelf processes. Dye recycling, from the inner-shelf back to the surfzone, is suggested by relatively long surfzone dye residence times.

}, keywords = {california, continental-shelf, internal tidal bores, nearshore, new-england shelf, ocean, rip currents, southern, transport, turbulence, zone}, isbn = {2169-9275}, doi = {10.1002/2013jc009722}, url = {Aerial images are used to quantify the concentration of fluorescent Rhodamine water tracing (WT) dye in turbid and optically deep water. Tracer releases near the shoreline of an ocean beach and near a tidal inlet were observed with a two-band multispectral camera and a pushbroom hyperspectral imager, respectively. The aerial observations are compared with near-surface in situ measurements. The ratio of upwelling radiance near the Rhodamine WT excitation and emission peaks varies linearly with the in situ dye concentrations for concentrations \<20ppb (r(2) = 0.70 and r(2) = 0.85-0.88 at the beach and inlet, respectively). The linear relationship allows for relative tracer concentration estimates without in situ calibration. The O(1 m) image pixels resolve complex flow structures on the inner shelf that transport and mix tracer.

}, keywords = {diffusion, phytoplankton, surf zone, Tracers, water}, isbn = {0739-0572}, doi = {10.1175/jtech-d-13-00230.1}, url = {Concurrent Lagrangian and Eulerian observations of rotational, low-frequency (10(-4) to 10(-2) Hz) surfzone eddies are compared. Surface drifters were tracked for a few hours on each of 11 days at two alongshore uniform beaches. A cross-shore array of near-bottom current meters extended from near the shoreline to seaward of the surfzone (typically 100 m wide in these moderate wave conditions). Lagrangian and Eulerian mean alongshore velocities V are similar, with a midsurfzone maximum. Cross-shore dependent Lagrangian (sigma(L)) and Eulerian (sigma(E)) rotational eddy velocities, estimated from low-pass filtered drifter and current meter velocities, respectively, also generally agree. Cross-shore rotational velocities have a midsurfzone maximum whereas alongshore rotational velocities are distributed more broadly. Daily estimates of the Lagrangian time scale, the time for drifter velocities to decorrelate, vary between 40 and 300 s, with alongshore time scales greater than cross-shore time scales. The ratio of Lagrangian to apparent Eulerian current meter decorrelation times T-L/T-A varies considerably, between about 0.5 and 3. Consistent with theory, some of the T-L/T-A variation is ascribable to alongshore advection and T-L/T-A is proportional to V/sigma, which ranges between about 0.6 and 2.5. Estimates of T-L/T-A vary between days with similar V/sigma suggesting that surfzone Lagrangian particle dynamics vary between days, spanning the range from "fixed-float{\textquoteright}{\textquoteright} to "frozen-field{\textquoteright}{\textquoteright} [Lumpkin et al., 2002], although conclusions are limited by the statistical sampling errors in both T-L/T-A and V/sigma.

}, keywords = {beach, currents, diffusivity, dispersion, drifter observations, nearshore, north-atlantic, southern-ocean, transport, waves}, isbn = {2169-9275}, doi = {10.1002/2013jc009415}, url = {We compare ground motions observed within about 100 m of the waterline on eight sites located on shorelines with different morphologies (rock slope, cliff, and sand beaches). At all sites, local ocean waves generated ground motions in the frequency band 0.01-40 Hz. Between about 0.01 and 0.1 Hz, foreshore loading and gravitational attraction from ocean swell and infragravity waves drive coherent, in-phase ground flexing motions mostly oriented cross-shore that decay inland. At higher frequencies between 0.5 and 40 Hz, breaking ocean waves and wave-rock impacts cause ground shaking. Overall, seismic spectral shapes were generally consistent across shoreline sites and usually within a few orders of magnitude despite the diverse range of settings. However, specific site response varied and was influenced by a combination of tide level, incident wave energy, site morphology, ground composition, and signal decay. Flexing and shaking increased with incident wave energy and was often tidally modulated, consistent with a local generation source. Flexing magnitudes were usually larger than shaking, and flexing displacements of several mm were observed during relatively large incident wave conditions (Hs 4-5 m). Comparison with traffic noise and earthquakes illustrate the relative significance of local ocean-generated signals in coastal seismic data. Seismic observations are not a simple proxy for wave-cliff interaction.

}, keywords = {beach, cliff, coast, coastal, island, nearshore, new-zealand, noise, platform, platforms, seismometer, wave impacts, wave loading}, isbn = {2169-9275}, doi = {10.1002/2013jc008883}, url = {Surveys of the subaerial beach (e.g., landward of approximately the MSL depth contour) are widely used to evaluate temporal changes in sand levels over large alongshore reaches. Here, seasonal beach face volume changes based on full bathymetry beach profiles (to similar to 8 m in depth) are compared with estimates based on the subaerial section of the profile. The profiles span 15 years and 75 km of Southern California shoreline, where seasonal vertical fluctuations in near-shore sand levels of a few meters are common. In years with relatively low winter wave energy, most erosion occurs above the MSL contour, and subaerial surveys capture as much as 0.8 of the total (relatively small) seasonal beach face volume change. In response to more energetic winter waves, beach face erosion increases and occurs as deep as 3 m below MSL, and subaerial surveys capture as little as 0.2 of the total beach face volume change. Patchy, erosion-resistant rock and cobble layers contribute to alongshore variation of the subaerial fraction of beach face volume change.

}, isbn = {0739-0572}, url = {A beach nourishment with approximately 1/3 fine-grained sediment (fines; particle diameter \<63 mu m) by mass was performed at Southern California{\textquoteright}s Border Fields State Park (BFSP). The nourishment was found to briefly (\<1 day) increase concentrations of surf-zone fecal indicator bacteria (FIB) above single-sample public health standards [104 most probable number (MPN).(100 mL)(-1)] but had no effect on phytoplankton. Contamination was constrained to the nourishment site: waters 300 m north or south of the nourishment were always below single-sample and geometric mean [\<= 35 MPN.(100 mL)(-1)] standards. Nourishment fines were identified as a source of the fecal indicator Enterococcus; correlations between fines and enterococci were significant (p \< 0.01), and generalized linear model analysis identified fines as the single best predictor of enterococci. Microcosm experiments and field sampling suggest that the short surf-zone residence times observed for enterococci (e-folding time 4 h) resulted from both rapid, postplacement FIB inactivation and mixing/transport by waves and alongshore currents. Nourishment fines were phosphate-rich/nitrogen-poor and were not correlated with surf-zone phytoplankton concentrations, which may have been nitrogen-limited.

}, keywords = {california, coastal waters, Fecal indicator bacteria, hepatitis-a virus, huntington-beach, marine beach, southern, sunlight inactivation, surf-zone, tijuana-estuary, urban runoff}, isbn = {0013-936X}, doi = {10.1021/es400572k}, url = {A suite of physical-biological models was used to explore the importance of mortality and fluid dynamics in controlling concentrations of fecal indicator bacteria (FIB) at Huntington Beach, CA. An advection-diffusion (AD) model provided a baseline to assess improvements in model skill with the inclusion of mortality. Six forms of mortality were modeled. All mortality models performed better than the AD model, especially at offshore sampling stations, where model skill increased from \<0.18 to \>0.50 (Escherichia colt) or \<-0.14 to \>0.30 (Enterococcus). Models including cross-shore variable mortality rates reproduced FIB decay accurately (p \< 0.05) at more stations than models without. This finding is consistent with analyses that revealed cross-shore variability in Enterococcus species composition and solar dose response. No best model was identified for Entero coccus, as all models including cross-shore variable mortality performed similarly. The best model for E. colt included solar-dependent and cross-shore variable mortality. (C) 2012 Elsevier Ltd. All rights reserved.

}, keywords = {advection, california, diffusion, enteric bacteria, enterococcus-faecalis, escherichia-coli, Fecal indicator bacteria, indicator bacteria, marine beach, mortality, solar-radiation, sunlight inactivation, surf zone, Surfzone, zone water-quality}, isbn = {0025-326X}, doi = {10.1016/j.marpolbul.2012.09.003}, url = {We present results from a 5-h field program (HB06) that took place at California{\textquoteright}s Huntington State Beach. We assessed the importance of physical dynamics in controlling fecal indicator bacteria (FIB) concentrations during HB06 using an individual based model including alongshore advection and cross-shore variable horizontal diffusion. The model was parameterized with physical (waves and currents) and bacterial (Escherichia coli and Enterococcus) observations made during HB06. The model captured surfzone FIB dynamics well (average surfzone model skill: 0.84 {E. coli) and 0.52 {Enterococcus)), but fell short of capturing offshore FIB dynamics. Our analyses support the hypothesis that surfzone FIB variability during HB06 was a consequence of southward advection and diffusion of a patch of FIB originating north of the study area. Offshore FIB may have originated from a different, southern, source. Mortality may account for some of the offshore variability not explained by the physical model. (C) 2012 Elsevier Ltd. All rights reserved.

}, keywords = {advection, budget analysis, california, diffusion, enterococci, escherichia-coli, Fecal indicator bacteria, huntington-beach, lake-michigan, marine beach, sunlight inactivation, surf-zone, Surfzone, zone water-quality}, isbn = {0025-326X}, doi = {10.1016/j.marpolbul.2012.09.030}, url = {Ground motions at the frequencies (between 0.01 and 0.1 Hz) of ocean infragravity and swell waves were observed on a cross-shore transect extending landward from the edge of a southern California coastal cliff. Cliff top ground motions are coherent and in phase with water level fluctuations at the cliff base. Vertical ground motions at infragravity and single frequencies decay rapidly with inland distance from the cliff edge (e-folding scale is about 12 m), and at the edge decrease by several orders of magnitude between high tide when waves reach the cliff base, and low tide when the waterline is about 50 m from the cliff base. The observed cross-shore decay scales are qualitatively consistent with gravitational loading and attraction of water waves at tidally modulated distances from the cliff base. At approximately constant distance from the waterline, ground motions vary roughly linearly with nearshore swell wave energy. In contrast to these locally forced ground motions, double frequency band (0.1-0.2 Hz) cliff top vertical ground motions are remotely generated with spatially uniform magnitudes approximately equal to those observed 14 km inland. Near the cliff edge, ground tilt dominates the observed large (relative to vertical) cross-shore acceleration at infragravity frequencies, contributes significantly to cross-shore acceleration at swell frequencies, and is a small fraction of cross-shore acceleration at higher frequencies.

}, keywords = {0.005-0.05 hz motions, climate, coastal, deformation, microseisms, oscillations, pacific, seismic noise, Seismology, shelves}, isbn = {0148-0227}, doi = {10.1029/2012jc007908}, url = {Wave breaking across the surf zone elevates the mean water level at the shoreline (setup), and drives fluctuations about the mean (runup). Runup often is divided into sea-swell (0.04-0.3 Hz) and lower frequency infragravity (0.00-0.04 Hz) components. With energetic incident waves, runup is dominated by infragravity frequencies, and total water levels (combined setup and runup) can exceed 3 m, significantly contributing to coastal flooding and erosion. Setup and runup observations on sandy beaches are scattered about empirical parameterizations based on near-shoreline beach slope and deep water wave height and wavelength. Accurate parameterizations are needed to determine flooding and erosion risk to coastal ecosystems and communities. Here, numerical simulations with the Boussinesq wave model funwaveC are shown to statistically reproduce typical empirical setup and runup parameterizations. Furthermore, the model infragravity runup R-s((ig)) strongly depends on the incident wave directional and frequency spread (about the mean direction and peak frequency). Realistic directional spread variations change R-s((ig)) equivalent to a factor of two variation in incident wave height. The modeled R-s((ig)) is shown to vary systematically with a new, non-dimensional spreading parameter that involves peak frequency, frequency spread, and directional spread. This suggests a new parameterization for R-s((ig)) potentially useful to predict coastal flooding and erosion. Citation: Guza, R. T., and F. Feddersen (2012), Effect of wave frequency and directional spread on shoreline runup, Geophys. Res. Lett., 39, L11607, doi:10.1029/2012GL051959.

}, keywords = {equations, generation, natural beach, nearshore, propagation, swash}, isbn = {0094-8276}, doi = {10.1029/2012gl051959}, url = {Ground motions atop a southern California, USA coastal cliff are compared with water level fluctuations observed at the cliff base, and with ground motions observed 10 km inland. At high tide, cliff top ground motions in three frequency bands were generated locally by ocean waves at the cliff base: (1) high-frequency (\>0.3 Hz) "shaking" caused by waves impacting the cliff, and (2) gravitational loading-induced "swaying" at the frequency of the incident sea swell waves (0.05-0.1 Hz), and (3) slow "swaying" at infragravity frequencies (0.006-0.05 Hz). At high tide, at infragravity and incident sea swell wave frequencies, cliff top vertical ground displacement and cliff base water level fluctuations are coherent and oscillate in phase (with occasional deviation at sea swell frequencies), and spectral levels at the cliff top are much higher than at the inland seismometer. In contrast, at "double frequencies" (0.1-0.3 Hz) spectral levels of vertical motions are nearly identical inland and at the cliff top, consistent with a common (distant or spatially distributed) source. At low tide, when ocean waves did not reach the cliff base, power levels of vertical ground motions at the cliff top decreased to inland levels at incident wave frequencies and higher, and only infragravity-band motions were noticeably forced by local ocean waves.

}, keywords = {climate, deformation, models, noise, pacific, Seismology, shelves, station, Tide, tsunami}, isbn = {0148-0227}, doi = {10.1029/2011jc007175}, url = {A model that accurately simulates surf zone waves, mean currents, and low-frequency eddies is required to diagnose the mechanisms of surf zone tracer transport and dispersion. In this paper, a wave-resolving time-dependent Boussinesq model is compared with waves and currents observed during five surf zone dye release experiments. In a companion paper, Clark et al. (2011) compare a coupled tracer model to the dye plume observations. The Boussinesq model uses observed bathymetry and incident random, directionally spread waves. For all five releases, the model generally reproduces the observed cross-shore evolution of significant wave height, mean wave angle, bulk directional spread, mean alongshore current, and the frequency-dependent sea surface elevation spectra and directional moments. The largest errors are near the shoreline where the bathymetry is most uncertain. The model also reproduces the observed cross-shore structure of rotational velocities in the infragravity (0.004 \< f \< 0.03 Hz) and very low frequency (VLF) (0.001 \< f \< 0.004 Hz) bands, although the modeled VLF energy is 2-3 times too large. Similar to the observations, the dominant contributions to the modeled eddy-induced momentum flux are in the VLF band. These eddies are elliptical near the shoreline and circular in the mid surf zone. The model-data agreement for sea swell waves, low-frequency eddies, and mean currents suggests that the model is appropriate for simulating surf zone tracer transport and dispersion.

}, keywords = {alongshore currents, beach, breaking, gravity-waves, longshore currents, nearshore, nonlinear boussinesq model, rip currents, shear instabilities, vertical structure}, isbn = {0148-0227}, doi = {10.1029/2011jc007210}, url = {Five surf zone dye tracer releases from the HB06 experiment are simulated with a tracer advection diffusion model coupled to a Boussinesq surf zone model (funwaveC). Model tracer is transported and stirred by currents and eddies and diffused with a breaking wave eddy diffusivity, set equal to the breaking wave eddy viscosity, and a small (0.01 m(2) s(-1)) background diffusivity. Observed and modeled alongshore parallel tracer plumes, transported by the wave driven alongshore current, have qualitatively similar cross-shore structures. Although the model skill for mean tracer concentration is variable (from negative to 0.73) depending upon release, cross-shore integrated tracer moments (normalized by the cross-shore tracer integral) have consistently high skills (approximate to 0.9). Modeled and observed bulk surf zone cross-shore diffusivity estimates are also similar, with 0.72 squared correlation and skill of 0.4. Similar to the observations, the model bulk (absolute) cross-shore diffusivity is consistent with a mixing length parameterization based on low-frequency (0.001-0.03 Hz) eddies. The model absolute cross-shore dispersion is dominated by stirring from surf zone eddies and does not depend upon the presence of the breaking wave eddy diffusivity. Given only the bathymetry and incident wave field, the coupled Boussinesq-tracer model qualitatively reproduces the observed cross-shore absolute tracer dispersion, suggesting that the model can be used to study surf zone tracer dispersion mechanisms.

}, keywords = {currents, drifter, turbulence, waves}, isbn = {0148-0227}, doi = {10.1029/2011jc007211}, url = {The sudden appearance at the surface of an alongshore-parallel band of red tide near Huntington Beach, California, is described in high spatial and temporal resolution using novel instrumentation including a global positioning system-tracked jet-ski. The scale of the surface chlorophyll a (Chl a) band was small (similar to 200 m cross-shore) and ephemeral (3 h) compared with the subsurface extent of the red tide (similar to 2 km, \> 7 d). The red tide was dominated by the regionally common dinoflagellate Lingulodinium polyedrum (F. Stein) and had developed as a subsurface Chl a layer during the 7 d prior to the surface appearance. A few hours before the surface appearance, a subsurface patch of elevated Chl a (Chl a \> 30 mu g L(-1)) was observed in 13-m total depth in the trough of a shoreward-propagating internal wave, consistent with dinoflagellate vertical swimming interacting with the internal wave-driven convergence. Internal wave-breaking-induced vertical mixing in similar to 8-m water depth vertically spread the Chl a patch to the surface, creating the alongshore surface band similar to 500 m from shore. Both the subsurface Chl a patch and the surface Chl a band were prevented from entering the surf-zone by a density barrier of warm water adjacent to the beach. These high-resolution observations emphasize the role of nearshore physical dynamics in controlling the duration and intensity of red tide exposure to coastal habitats.

}, keywords = {algal, bacteria, blooms, coastal waters, currents, frequency internal waves, layers, marsh, phytoplankton, southern california, transport}, isbn = {0024-3590}, doi = {10.4319/lo.2011.56.3.0787}, url = {SWAN model predictions, initialized with directional wave buoy observations in 550-m water depth offshore of a steep, submarine canyon, are compared with wave observations in 5.0-, 2.5-, and 1.0-m water depths. Although the model assumptions include small bottom slopes, the alongshore variations of the nearshore wave field caused by refraction over the steep canyon are predicted well over the 50 days of observations. For example, in 2.5-m water depth, the observed and predicted wave heights vary by up to a factor of 4 over about 1000 m alongshore, and wave directions vary by up to about 10, sometimes changing from south to north of shore normal. Root-mean-square errors of the predicted wave heights, mean directions, periods, and radiation stresses (less than 0.13 m, 5 degrees, 1 s, and 0.05 m(3)/s(2) respectively) are similar near and far from the canyon. Squared correlations between the observed and predicted wave heights usually are greater than 0.8 in all water depths. However, the correlations for mean directions and radiation stresses decrease with decreasing water depth as waves refract and become normally incident. Although mean wave properties observed in shallow water are predicted accurately, nonlinear energy transfers from near-resonant triads are not modeled well, and the observed and predicted wave energy spectra can differ significantly at frequencies greater than the spectral peak, especially for narrow-band swell. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {beach, boussinesq equations, breaking, coastal regions, linear dispersion characteristics, model, modeling, refraction, refraction-diffraction, surface gravity-waves, transformation, verification, waves}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2011.01.013}, url = {The effect of using time-averaged wave statistics in a simple empirical model for shoreline change is investigated. The model was first calibrated with a six-year time series of hourly wave conditions and weekly shoreline position at the Gold Coast Australia. The model was then recalibrated with the hourly waves averaged over intervals up to 1 year. With wave averaging up to 2 days, model performance was approximately constant (squared correlation r(2)similar to 0.61-0.62), with only small changes in the values of empirical model parameters (e.g. the beach response coefficient c varied by less than 4\%). With between 2 and 40 day averaging, individual storms are not resolved; model skill decreased only modestly ( r(2)similar to 0.55), but c varied erratically by up to 40\% of the original value. That is, optimal model coefficients depend on wave averaging, an undesirable result. With increased averaging (\>40 days) seasonal variability in the wave field is not resolved well and model skill declined markedly. Thus, temporal averaging of wave conditions increases numerical efficiency, but over-averaging degrades model performance and distorts best-fit values of model free parameters. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {Argus, model, prediction, Shoreline, video, Wave averaging}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2011.03.007}, url = {Four years of beach elevation surveys at Ocean Beach, San Francisco, California, are used to extend an existing equilibrium shoreline change model, previously calibrated with fine sand and moderate energy waves, to medium sand and higher-energy waves. The shoreline, characterized as the cross-shore location of the mean high water contour, varied seasonally by between 30 and 60 m, depending on the alongshore location. The equilibrium shoreline change model relates the rate of horizontal shoreline displacement to the hourly wave energy E and the wave energy disequilibrium, the difference between E and the equilibrium wave energy that would cause no change in the present shoreline location. Values for the model shoreline response coefficients are tuned to fit the observations in 500 m alongshore segments and averaged over segments where the model has good skill and the estimated effects of neglected alongshore sediment transport are relatively small. Using these representative response coefficients for 0.3 mm sand from Ocean Beach and driving the model with much lower-energy winter waves observed at San Onofre Beach (also 0.3 mm sand) in southern California, qualitatively reproduces the small seasonal shoreline fluctuations at San Onofre. This consistency suggests that the shoreline model response coefficients depend on grain size and may be constant, and thus transportable, between sites with similar grain size and different wave climates. The calibrated model response coefficients predict that for equal fluctuations in wave energy, changes in shoreline location on a medium-grained (0.3 mm) beach are much smaller than on a previously studied fine-grained (0.2 mm) beach.

}, keywords = {duck, erosion, model, north-carolina, prediction, profiles, surf zones, variability}, isbn = {0148-0227}, doi = {10.1029/2010jc006681}, url = {The frequency, spatial distribution, and dimensions of coastal cliff retreats, a basic statistic underlying cliff top hazard assessment, are presented for 7.1 km of unprotected and slowly retreating coastal cliffs near Point Loma in San Diego, California, US. Using 8 airborne light detection and ranging (lidar) surveys collected over 5.5 years, 130 individual cliff edge failures (primarily rockfalls, block falls, and topples) were detected. Footprint areas varied from 3 to 268 m(2), maximum landward retreats from 0.8 to 10 m, and alongshore lengths from 2 to 68 m. The failures with the largest landward retreats were also relatively long, and 13\% of the slides accounted for 50\% of the lost cliff area over the study period. On this short (5.5 years) time scale, "no change" was the most common observation (84\% of the cliff edge). Probability distributions of non-zero cliff retreat during each time interval usually had a single peak between 1 and 2.5 m. Intervals with high mean retreat had elevated numbers of failure in all class sizes, and also contained the largest individual retreats. Small and medium slides tended to reoccur preferentially (relative to randomly) near previous small and medium slides, forming short-term hot spots, while large slides were less likely to reoccur near previous large slides. Cumulative distributions of landslide failure parameters (area, mean retreat, maximum retreat, and length) follow an inverse power-law for medium to large size events, similar to previously reported distributions of coastal and inland landsliding.

}, keywords = {distributions, erosion, failure, holderness coast, instability, landslides, magnitude-frequency, prediction, recession, sea-cliffs}, isbn = {1561-8633}, doi = {10.5194/nhess-11-205-2011}, url = {Cross-shore surfzone tracer dispersion in a wave driven alongshore current is examined over a range of wave and current conditions with 6 continuous dye releases, each roughly 1-2 hours in duration, at Huntington Beach, California. Fluorescent dye tracer released near the shoreline formed shore parallel plumes that were sampled on repeated cross-shore transects with a jet ski mounted fluorometer. Ensemble averaged cross-shore tracer concentration profiles are generally shoreline attached (maximum at or near the shoreline), with increasing cross-shore widths and decreasing peak values with downstream distance. More than a few 100 m from the source, tracer is often well mixed across the surfzone (i. e., saturated) with decreasing tracer concentrations farther seaward. For each release, cross-shore surfzone absolute diffusivities are estimated using a simple Fickian diffusion solution with a no-flux boundary at the shoreline, and range from 0.5-2.5 m(2) s(-1). Surfzone diffusivity scalings based on cross-shore bore dispersion, surfzone eddy mixing length, and undertow driven shear dispersion are examined. The mixing-length scaling has correlation r(2) = 0.59 and the expected best-fit slope \< 1, indicating that horizontal rotational motions are important for cross-shore tracer dispersion in the surfzone.

}, keywords = {beach, california, flow, plume, water-quality, waves, zone}, isbn = {0148-0227}, doi = {10.1029/2009jc005683}, url = {The coarse sediment fraction of geologic formations exposed in 42 km of southern California seacliffs in the Oceanside Littoral Cell was estimated using more than 400 samples An impulse laser, oblique photographs, and coastal maps were used to define thickness and alongshore extent of the geologic units exposed in the seacliffs The coarse sediment (defined as diameter \> 0 06 mm) fraction in each geologic unit was estimated by sieving About 80\% of the exposed cliff face is coarse and can contribute to beach building Finer cliff sediments are transported offshore by waves and currents Although there are some differences, the observed 80\% coarse fraction is generally consistent with previous estimates based on an order of magnitude fewer samples Coastal development has largely eliminated about 40\% of seacliffs in the Oceanside Littoral Cell as potential beach sand sources For the remaining seacliffs, 1 cm of average cliff retreat yields 10,000 m(3) of potential beach-building material

}, keywords = {california, Cliffs, Coastal erosion, sediment budget, southern california}, isbn = {0749-0208}, doi = {10.2112/08-1179.1}, url = {Seacliff changes evaluated using both terrestrial and airborne lidar are compared along a 400 m length of coast in Del Mar, California. The many large slides occurring during the rainy, six-month study period (September 2004 to April 2005) were captured by both systems, and the alongshore variation of cliff face volume changes estimated with the airborne and terrestrial systems are strongly correlated (r(2) = 0.95). However, relatively small changes in the cliff face are reliably detected only with the more accurate terrestrial lidar, and the total eroded volume estimated with the terrestrial system was 30 percent larger than the corresponding airborne estimate. Although relatively small cliff changes are not detected, the airborne system can rapidly survey long cliff lengths and provides coverage on the cliff top and beach at the cliff base.

}, keywords = {cliff erosion, coastal, evolution, photogrammetry}, isbn = {0099-1112}, url = {Shoreline location and incident wave energy, observed for almost 5 years at Torrey Pines beach, show seasonal fluctuations characteristic of southern California beaches. The shoreline location, defined as the cross-shore position of the mean sea level contour, retreats by almost 40 m in response to energetic winter waves and gradually recovers during low-energy summer waves. Hourly estimates of incident wave energy and weekly to monthly surveys of the shoreline location are used to develop and calibrate an equilibrium-type shoreline change model. By hypothesis, the shoreline change rate depends on both the wave energy and the wave energy disequilibrium with the shoreline location. Using calibrated values of four model free parameters, observed and modeled shoreline location are well correlated at Torrey Pines and two additional survey sites. Model free parameters can be estimated with as little as 2 years of monthly observations or with about 5 years of ideally timed, biannual observations. Wave energy time series used to calibrate and test the model must resolve individual storms, and model performance is substantially degraded by using weekly to monthly averaged wave energy. Variations of free parameter values between sites may be associated with variations in sand grain size, sediment availability, and other factors. The model successfully reproduces shoreline location for time periods not used in tuning and can be used to predict beach response to past or hypothetical future wave climates. However, the model will fail when neglected geologic factors are important (e.g., underlying bedrock limits erosion or sand availability limits accretion).

}, keywords = {erosion, nearshore, north-carolina, prediction, profiles, sediment transport, sheet flow, surf zones, time-dependent beach, variability}, isbn = {0148-0227}, doi = {10.1029/2009jc005359}, url = {Seacliff retreat has been variously characterized as the recession rate of the cliff top, of the cliff base, and as the bulk recession rate based on volumetric changes of the entire cliff face. Here, these measures of retreat are compared using nine semi-annual airborne LiDAR (Light Detection And Ranging) surveys of southern California seacliffs. Changes in the cliff base location (where the steeply sloping cliff face intersects the beach) include cliff retreat owing to basal erosion, but also reflect changes in beach sand level and basal talus deposits. Averaged over the 2.5 km alongshore study span, the cliff base actually prograded seaward about 12 cm during the 4-year study. Cliff top change was dominated by few, relatively large (several meters) localized retreats. Cliff face changes, that include failures and deposits anywhere on the cliff profile, had a relatively small mean magnitude compared to cliff top changes and were more widely distributed alongshore. However, the similar alongshore averaged. cumulative cliff top and net bulk cliff face end-point retreat (14 and 19 cm, respectively) suggest that mean cumulative cliff top retreat can potentially be a viable surrogate for mean net cumulative cliff-wide erosion (and vice versa) over relatively short time periods. Cliff face erosion occurred repeatedly at some locations, confirming the presence of seacliff erosion hot-spots during the study period. (C) 2009 Elsevier B.V. All rights reserved.

}, keywords = {change, coastal cliff erosion, Coastal erosion, detection, LIDAR, Seacliff retreat, southern california}, isbn = {0169-555X}, doi = {10.1016/j.geomorph.2009.06.018}, url = {Decisions about recreational beach closures would be enhanced if better estimates of surfzone contaminant transport and dilution were available. In situ methods for measuring fluorescent Rhodamine WT dye tracer in the surfzone are presented, increasing the temporal and spatial resolution over previous surfzone techniques. Bubbles and sand suspended by breaking waves in the surfzone interfere with in situ optical fluorometer dye measurements, increasing the lower bound for dye detection (a parts per thousand 1 ppb) and reducing (quenching) measured dye concentrations. Simultaneous turbidity measurements are used to estimate the level of bubble and sand interference and correct dye estimates. After correction, root-mean-square dye concentration errors are estimated to be \< 5\% of dye concentration magnitude, thus demonstrating the viability of in situ surfzone fluorescent dye measurements. The surfzone techniques developed here may be applicable to other environments with high bubble and sand concentrations (e.g., cascading rivers and streams).

}, keywords = {air entrainment, breaking waves, diffusion, dispersion, Fluorescent dye, Fluorometer, measurement, mixing, model, Surfzone, suspended-sediment, transport, Turbidity, zone}, isbn = {0049-6979}, doi = {10.1007/s11270-009-0030-z}, url = {A four-year time series of nine airborne LiDAR surveys were used to assess the roles of wave attack and rainfall on the erosion of 42 km of southern California seacliffs. Nine continuous seacliff sections, separated by coastal lagoon mouths, all show maximum seacliff erosion in the rainiest time period (when wave energy was not particularly elevated), and in most sections the squared correlations between rainfall and erosion time series exceeded 0.8. Although rain and associated subaerial mechanisms such as groundwater seepage triggered most of the observed seacliff failures, wave attack accelerated seacliff erosion, with erosion rates of cliffs exposed to wave attack five times higher than at adjacent cliffs not exposed to waves. The results demonstrate the importance of both waves and rain in the erosion of southern California seacliffs and suggest that the combined influences of marine and subaerial processes accelerate the erosion rate through positive feedbacks. (C) 2009 Elsevier B.V. All rights reserved.

}, keywords = {california, cliff erosion, Coastal erosion, coastal landslides, el-nino, events, instability, LiDAR, San Diego County, retreat, runup, Seacliff retreat, Shoreline}, isbn = {0025-3227}, doi = {10.1016/j.margeo.2009.08.008}, url = {Torrey Pines State Beach, a site with large seasonal fluctuations in sand level, received a small shoreface beach fill (about 160,000 m(3)) in April 2001. The 600 m-long, flat-topped nourishment pad extended from a highway riprap revetment seaward about 60 m, terminating in a 2 m-tall vertical scarp. A 2.7 km alongshore span, centered on the nourishment region, was monitored prior to the nourishment and biweekly to monthly for the following 2 years. For the first 7 months after the nourishment, through fall 2001, significant wave heights were small, and the elevated beach fill remained in place, with little change near and above Mean Sea Level (MSL). In contrast, the shoreline accreted on nearby control beaches following a seasonal pattern common in southern California, reducing the elevation difference between the nourished and adjacent beaches. During the first winter storm (3 m significant wave height), the shoreline retreated rapidly over the entire 2.7 km survey reach, forming an alongshore-oriented sandbar in 3 to 4 m water depth [Seymour, RJ., Guza, R.T., O{\textquoteright}Reilly, W., Elgar, S., 2004. Rapid erosion of a Southern California beach fill. Coastal Engineering 52 (2),151-158.]. We show that the winter sandbar, most pronounced offshore of the nourishment, moved back onto the beach face during summer 2002 (following the usual seasonal pattern) and formed a wider beach above MSL at the site of the original nourishment than on the control beaches. Thus, the April 2001 shoreline nourishment was detectable until late fall 2002, persisting locally over a full seasonal cycle. In an extended 7-year time series, total sand volumes (summed between the back beach and 8 m water depth, over the entire 2.7 km reach) exhibit multi-year fluctuations of unknown origin that are twice as large as the nourishment volume. (C) 2008 Elsevier B.V. All rights reserved.

}, keywords = {beach, beach fill, beach nourishment, erosion, monitoring, shore nourishment, Torrey Pines, waves}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2008.11.004}, url = {Continuous chlorophyll-a (Chla) measurements in the surfzone (region of wave-breaking adjacent to the shoreline) would increase understanding of harmful algal blooms, food supply for intertidal invertebrates and fishes, and the fate of terrestrial runoff pollution. Optical measurements of Chla fluorescence in the surfzone are affected by bubbles and suspended sand. Here, errors in surfzone Chla fluorescence measurements (using WET Labs ECO Triplet fluorometers) are estimated by comparing observed (Chla(raw)) with known (Chla(true)) Chla concentrations in laboratory tests with controlled amounts of bubbles and suspended sand (characterized with concurrently measured optical turbidity, tau). For both bubbles and sand, Chla raw and t are linearly correlated, and the regression line slope depends on Chla(true). When Chla(true) is low, Chla(raw) is biased high, and when Chla(true) is high, Chla(raw) is biased low. Fluorometers were also deployed in a natural surfzone, and for the limited range of field Chla observed, the field and laboratory tau-Chla relationships were largely consistent. Mechanisms responsible for these biases are proposed, and correction procedures using the observed tau-Chla relationship are developed and applied to surfzone Chla(raw) observations. For the moderate Chla(true) concentrations (2-4 mu g L(-1)) encountered, errors in hourly mean and instantaneous Chla(raw) are less than 5\% and 15\%, respectively. Larger errors are expected for Chla(true) outside this range. Although further testing is needed, the results suggest that in situ, optical Chla(raw) from other turbid environments (e.g., estuaries, bays) should also be interpreted cautiously.

}, keywords = {breaking waves, entrainment, ocean, suspended-sediment, zone}, isbn = {1541-5856}, doi = {10.4319/lo.2011.56.3.0787}, url = {Surfzone dispersion is characterized with single-particle Lagrangian statistics of GPS-tracked drifters deployed on 5 days at Huntington Beach, California. Incident wave heights varied weakly between days, and stationary rip currents did not occur. Generally, the time-dependent bulk surfzone cross-shore diffusivity kappa(xx) was similar on all days, reaching a local maxima of approximately 1.5 m(2) s(-1) between 160 and 310 s, before decreasing to about 1 m(2) s(-1) at 1000 s. The alongshore diffusivity kappa(yy) increased monotonically to 1000 s and was variable between the 5 days. For times greater than 30 s, the alongshore diffusivity is greater than the cross-shore diffusivity, consistent with previous observations. The observed diffusivities are fit to analytic functional forms, from which asymptotic diffusivities and Lagrangian timescales are determined. The asymptotic alongshore diffusivity (kappa) over cap (infinity)(yy) varies between 4 and 19 m(2) s(-1), and this variation is related to the variation in the maximum of the mean alongshore current (v) over bar (m), broadly consistent with a shear dispersion scaling (kappa) over cap (infinity)(yy) similar to (v) over bar (2)(m). Cross-shore variation in dispersion processes, lumped together in the bulk kappa, is apparent in the non-Gaussian probability distribution function of drifter displacements at intermediate times (30 s). Both biased and unbiased diffusivity sampling errors depend on the number and length of drifter trajectories and limit aspects of the analysis.

}, keywords = {atlantic, circulation, southern california, statistics, transport, turbulence, zone}, isbn = {0148-0227}, doi = {10.1029/2009jc005328}, url = {Airborne light detecting and ranging (lidar) systems can survey hundreds of kilometers of shoreline with high spatial resolution (several elevation estimates per square meter). Sequential surveys yield spatial change maps of beach and dune sand levels. However, lidar data include elevations of the exposed, subaerial beach and. seaward of the waterline, the ocean surface. Here, a simple method is developed to find the waterline and eliminate returns from the ocean surface. A vertical elevation cutoff is used, with the waterline elevation (W) above the known tide level because of the superelevation from wave setup and runup. During each lidar pass, the elevation cutoff (W) is assumed proportional (C) to the offshore significant wave height H-s. Comparison of in situ and lidar surveys on a moderately sloped, dissipative California beach yields C approximate to 0.4 which is qualitatively consistent with existing observations of runup and setup. The calibrated method rejects ocean surface data, while retaining subaerial beach points more than 70 m seaward of the mean high waterline, which is often used as a conservative default waterline.

}, keywords = {airborne topographic lidar, coastal, el-nino, erosion, florida, north-carolina, runup, setup, volumetric change, wave}, isbn = {0739-0572}, doi = {10.1175/2008jtecho561.1}, url = {To provide coastal engineers and scientists with a detailed inter-comparison of widely used parametric wave transformation models, several models are tested and calibrated with extensive observations from six field experiments on barred and unbarred beaches. Using previously calibrated ("default") values of a free parameter T, all models predict the observations reasonably well (median root-mean-square wave height errors are between 10\% and 20\%) at all field sites. Model errors can be reduced by roughly 50\% by tuning T for each data record. No tuned or default model provides the best predictions for all data records or at all experiments. Tuned T differ for the different models and experiments, but in all cases T increases as the hyperbolic tangent of the deep-water wave height, H.. Data from two experiments are used to estimate empirical, universal curves for T based on Ho. Using the new parameterization, all models have similar accuracy, and usually show increased skill relative to using default T. (c) 2007 Elsevier B.V. All rights reserved.

}, keywords = {dissipation, energy, nearshore, surf zone, Surfzone, transport, verification, water, wave breaking, wave models}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2007.10.002}, url = {The effect of alongshore variations in the incident wavefield on wave-driven setup and on alongshore flows in the surfzone is investigated using observations collected onshore of a submarine canyon. Wave heights and radiation stresses at the outer edge of the surfzone (water depth approximate to 2.5 m) varied by up to a factor of 4 and 16, respectively, over a 450 m alongshore distance, resulting in setup variations as large as 0.1 m along the shoreline (water depth approximate to 0.3 m). Even with this strong alongshore variability, wave-driven setup was dominated by the cross-shore gradient of the wave radiation stress, and setup observed in the surfzone is predicted well by a one-dimensional cross-shore momentum balance. Both cross-shore radiation stress gradients and alongshore setup gradients contributed to the alongshore flows observed in the inner surfzone when alongshore gradients in offshore wave heights were large, and a simplified alongshore momentum balance suggests that the large [O(1 kg/(s(2) m)] observed setup-induced pressure gradients can drive strong [O(1 m/s)] alongshore currents.

}, keywords = {beach, delilah, field observations, gravity-waves, longshore currents, momentum balances, nearshore, radiation, stress, surf zone, transformation}, isbn = {0148-0227}, doi = {10.1029/2007jc004514}, url = {[1] The propagation of infragravity waves ( ocean surface waves with periods from 20 to 200 s) over complex inner shelf ( water depths from about 3 to 50 m) bathymetry is investigated with field observations from the southern California coast. A wave-ray-path-based model is used to describe radiation from adjacent beaches, refraction over slopes ( smooth changes in bathymetry), and partial reflection from submarine canyons ( sharp changes in bathymetry). In both the field observations and the model simulations the importance of the canyons depends on the directional spectrum of the infragravity wave field radiating from the shoreline and on the distance from the canyons. Averaged over the wide range of conditions observed, a refraction-only model has reduced skill near the abrupt bathymetry, whereas a combined refraction and reflection model accurately describes the distribution of infragravity wave energy on the inner shelf, including the localized effects of steep-walled submarine canyons.

}, keywords = {beat, edge wave, field observations, generation, mean longshore-current, ocean, propagation, shear instabilities, surface gravity-waves, water-waves}, isbn = {0148-0227}, doi = {10.1029/2007jc004227}, url = {[1] Setup, the increase in the mean water level associated with breaking waves, observed between the shoreline and about 6-m water depth on an ocean beach is predicted well by a model that includes the effects of wave rollers and the bottom stress owing to the mean flow. Over the 90-day observational period, the measured and modeled setups are correlated ( squared correlation above 0.59) and agree within about 30\%. Although rollers may affect setup significantly on beaches with large-amplitude ( several meters high) sandbars and may be important in predicting the details of the cross-shore profile of setup, for the data discussed here, rollers have only a small effect on the amount of setup. Conversely, bottom stress ( calculated using eddy viscosity and undertow formulations based on the surface dissipation, and assuming that the eddy viscosity is uniform throughout the water column) significantly affects setup predictions. Neglecting bottom stress results in underprediction of the observed setup in all water depths, with maximum underprediction near the shoreline where the observed setup is largest.

}, keywords = {barred beaches, boundary-layer, breaking waves, cross-shore currents, field observations, longshore currents, natural beach, obliquely incident, radiation stress, surf-zone}, isbn = {0148-0227}, doi = {10.1029/2006jc003549}, url = {Surf-zone dispersion is studied using drifter observations collected within about 200 m of the shoreline (at depths of less than about 5 m) on a beach with approximately alongshore uniform bathymetry and waves. There were about 70 individual drifter releases, each 10-20 min in duration, on two consecutive days. On the first day, the sea-swell significant wave height H-s was equal to 0.5 m and mean alongshore currents vertical bar(v) over bar vertical bar were moderate (\<0.1 m s(-1)). On the second day, the obliquely incident waves were larger, with Hs equal to 1.4 m, and at some surf-zone locations vertical bar\<(v)over bar\>vertical bar was greater than 0.5 m s(-1). The one-particle diffusivity was larger, with larger waves and stronger currents. On both days, the one-particle diffusivity tensor is nonisotropic and time-dependent. The major axis is initially parallel to the cross-shore direction, but after a few wave periods it is aligned with the alongshore direction. In both the along-and cross-shore directions, the asymptotic diffusivity is reached sooner within, rather than seaward of, the surf zone. Two-particle statistics indicate that relative dispersion grows like D-2(t) similar to t(3/2) and that the relative diffusivity is scale-dependent as mu similar to l(2/3), with l being the particle separation. The observed scalings differ from 2D inertial-subrange scalings [D-2(t) similar to t(3) and mu similar to l(4/3)]. Separations have a non-Gaussian self-similar distribution that is independent of time. The two-particle statistics are consistent with a nonconstant-coefficient diffusion equation for the separation probability density functions. The dispersion is explained by neither irrotational surface gravity waves nor shear dispersion. The observations imply the existence of a 2D eddy field with 5-50-m length scales, the source of which is speculated to be alongshore gradients in breaking-wave height associated with finite crest lengths.

}, keywords = {2-dimensional turbulence, atlantic, circulation, coastal, currents, diffusion, ocean, southern california, Tracers, transport}, isbn = {0022-3670}, doi = {10.1175/2007jpo3580.1}, url = {The 25-m onshore migration of a nearshore sandbar observed over a 5-day period near Duck, NC, is simulated with a simplified, computationally efficient, wave-resolving single-phase model. The modeled sediment transport is assumed to occur close to the seabed and to be in phase with the bottom stress. Neglected intergranular stresses and fluid-granular interactions, likely important in concentrated flow, are compensated for with an elevated (relative to that appropriate for a clear fluid) model roughness height that gives the best fit to the observed bar migration. Model results suggest that when mean-current-induced transport is small, wave-induced transport leads to the observed onshore bar migration. Based on the results from the simplified phase-resolving model, a wave-averaged, energetics-type model (e.g., only moments of the near-bottom velocity field are required) with different friction factors for oscillatory and mean flows is developed that also predicts the observed bar migration. Although the assumptions underlying the models differ, the similarity of model results precludes determination of the dominant mechanisms of sediment transport during onshore bar migration. (C) 2006 Elsevier B.V. All rights reserved.

}, keywords = {beds, bottom, bottom stress, boundary-layer, evolution, model, natural beach, nearshore, roughness, sandbar migration, sediment transport, sheet flow, wave boundary layer}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2006.04.003}, url = {The strong tidal modulation of infragravity (200 to 20 s period) waves observed on the southern California shelf is shown to be the result of nonlinear transfers of energy from these low-frequency long waves to higher-frequency motions. The energy loss occurs in the surfzone, and is stronger as waves propagate over the convex low-tide beach profile than over the concave high-tide profile, resulting in a tidal modulation of seaward-radiated infragravity energy. Although previous studies have attributed infragravity energy losses in the surfzone to bottom drag and turbulence, theoretical estimates using both observations and numerical simulations suggest nonlinear transfers dominate. The observed beach profiles and energy transfers are similar along several km of the southern California coast, providing a mechanism for the tidal modulation of infragravity waves observed in bottom-pressure and seismic records on the continental shelf and in the deep ocean.

}, keywords = {beach, edge waves, excitation, field observations, mean longshore-current, motions, ocean, oscillations, shear instabilities, surface gravity-waves}, isbn = {0094-8276}, doi = {10.1029/2005gl025514}, url = {[1] Nonlinear energy transfers with sea and swell (frequencies 0.05-0.40 Hz) were responsible for much of the generation and loss of infragravity wave energy (frequencies 0.005-0.050 Hz) observed under moderate- and low-energy conditions on a natural beach. Cases with energetic shear waves were excluded, and mean currents, a likely shear wave energy source, were neglected. Within 150 m of the shore, estimated nonlinear energy transfers to ( or from) the infragravity band roughly balanced the divergence (or convergence) of the infragravity energy flux, consistent with a conservative energy equation. Addition of significant dissipation (requiring a bottom drag coefficient exceeding about 10(-2)) degraded the energy balance.

}, keywords = {beat, breaking waves, delilah, edge waves, motions, surface gravity-waves, water, zone}, isbn = {0148-0227}, doi = {10.1029/2006jc003539}, url = {Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell{\textquoteright}s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.

}, keywords = {energy, infragravity waves, instabilities, mean longshore-current, nearshore}, isbn = {0022-3670}, doi = {10.1175/jpo2890.1}, url = {Acoustic Doppler velocimeter measurements in the surfzone can be corrupted by bubbles and suspended sediment, lack of submergence during the passage of wave troughs, biofouling, blockage (e.g., from kelp on instrument mounting frames) of the flow field near the current meter or of the path between the sampled fluid volume and the acoustic transducers, and by insufficient distance between an accreting seafloor and the sample volume. Individual bad acoustic Doppler velocity values can be detected (and subsequently replaced) from low along-beam signal-to-noise ratios and from low coherence between successive acoustic returns used to estimate velocity. In addition, corrupted data runs can be identified from ratios of pressure to velocity variance that deviate from linear theory, and from low coherence between time series of collocated pressure and wave-orbital velocities. Unmeasured vertical tilts of a current meter can be estimated from horizontal and vertical velocities, and corrected for numerically.

}, keywords = {acoustic Doppler velocimeters, current profiler, current-meter, data quality, nearshore, performance, surface gravity-waves, surfzone instrumentation, surfzone waves and currents, turbulence}, isbn = {0957-0233}, doi = {10.1088/0957-0233/16/10/002}, url = {[1] Observations of shear waves, alongshore propagating meanders of the mean alongshore current with periods of a few minutes and alongshore wavelengths of a few hundred meters, are compared with model predictions based on numerical solutions of the nonlinear shallow water equations. The model ( after Ozkan-Haller and Kirby ( 1999)) assumes alongshore homogeneity and temporally steady wave forcing and neglects wave-current interactions, eddy mixing, and spatial variation of the ( nonlinear) bottom drag coefficient. Although the shapes of observed and modeled shear wave velocity spectra differ, and root-mean-square velocity fluctuations agree only to within a factor of about 3, aspects of the cross-shore structure of the observed ( similar to 0.5 - 1.0 m above the seafloor) and modeled ( vertically integrated) shear waves are qualitatively similar. Within the surf zone, where the mean alongshore current ( V) is strong and shear waves are energetic, observed and modeled shear wave alongshore phase speeds agree and are close to both V and C-lin ( the phase speed of linearly unstable modes) consistent with previous results. Farther offshore, where V is weak and observed and modeled shear wave energy levels decay rapidly, modeled and observed C diverge from C-lin and are close to the weak alongshore current V. The simulations suggest that the alongshore advection of eddies shed from the strong, sheared flow closer to shore may contribute to the offshore decrease in shear wave phase speeds. Similar to the observations, the modeled cross- and alongshore shear wave velocity fluctuations have approximately equal magnitude, and the modeled vorticity changes sign across the surf zone.

}, keywords = {alongshore currents, beaches, field observations, instabilities, mean longshore-current}, isbn = {0148-0227}, doi = {10.1029/2004jc002541}, url = {Estimates of the heights of large (0.1-0.4 m heights and 1-10 m horizontal lengths) migrating bedforms on a sandy beach made with fixed, single-point altimeters are similar to heights estimated from profiles across the bedforms made with altimeters mounted on an amphibious vehicle that traversed the surf zone. Unlike many profiling systems, the robust, fixed altimeters can measure bedforms in bubbly, sediment-laden surf zone waters nearly continuously, including during storms, thus allowing investigation of the relationships between bedform heights and near-bottom velocities to be extended to a wide range of wave conditions. The fixed-altimeter observations of migrating bedforms suggest a sandy surf zone seafloor is not always smooth during energetic conditions with strong mean currents and large wave-orbital velocities. (c) 2005 Elsevier B.V. All rights reserved.

}, keywords = {bed roughness, currents, dynamics, evolution, geometry, megaripples, migration, morphology, nearshore, ripples, roughness, sonar altimeters, surf zone, wave}, isbn = {0025-3227}, doi = {10.1016/j.margeo.2005.01.005}, url = {The infragravity wave (periods between roughly 20 and 200 s) energy balance in shallow, nearshore waters is believed to be effected by generation by groups of sea and swell, dissipation, shoreline reflection, and refractive trapping. Observations obtained with alongshore oriented arrays of current meters or pressure gauges have been previously used to identify concentrations of energy at the frequency-alongshore wavenumbers of refractively trapped edge waves, but seaward and shoreward propagating waves were not differentiated. Surfzone dissipation theoretically limits edge wave growth, and a different analysis (using the approximation of shore-normal propagation) shows that the energy flux of shoreward propagating infragravity waves decreases owing to surfzone dissipation. Here an estimator is developed that yields the alongshore wavenumber-frequency spectra of seaward and shoreward propagating waves, using the WKB approximation and observations from an alongshore-oriented array of pressure and velocity sensors. Example spectra, estimated using data from the spatially sparse and relatively short SandyDuck arrays, suggests that strong dissipation of shoreward propagating infragravity waves occurs over a wide range of alongshore wavenumbers, effectively suppressing the excitation of edge wave modes.

}, keywords = {beaches, beat, delilah, field observations, generation, infragravity waves, long, spectra, stress, surface gravity-waves, waves}, isbn = {0148-0227}, doi = {10.1029/2003jc002236}, url = {A winter storm eroded a small (160,000 m(3)) beach fill at Torrey Pines State Beach in southern California. The fill, constructed in April 2001, was a 600-m long flat-topped berm, extending from a highway revetment seaward about 80 m, terminating in a 2-m tall, near-vertical scarp. The size distributions of the preexisting and fill beach sand were similar (median similar to0.2 mm). A total of 56 cross-shore transects were surveyed between the revetment and 8 m water depth biweekly along 2.7 km of the beach centered on the fill area. During summer and fall, the incident significant wave heights measured 1 km offshore of the fill usually were below I m, the scarp was not overtopped, and the fill did not change greatly. The beach face alongshore of the fill accreted, consistent with the usual seasonal cycle in southern California. During a storm (3 m significant wave height) in late November, erosion began when wave uprushes overtopped the scarp and reached the relatively flat elevated fill, where the overwash flowed alongshore to initially small depressions that channeled the flow seawards. The offshore flow rapidly deepened and widened the channels, which maintained steep vertical faces and eroded by slumping. Thirty hours after the storm began, the shoreward end of the eroded channels had retreated to the highway revetment, leaving uneroded sand peninsulas protruding seawards similar to50 m from the revetment and elevated similar to1.75 m above the surrounding beach. Erosion of the beach adjacent to the fill was much less variable alongshore than within the fill region. During the next few days, the peninsulas eroded almost completely. (C) 2004 Elsevier B.V All rights reserved.

}, keywords = {beach fill, beach nourishment, erosion, surveying techniques, Torrey Pines Beach, waves}, isbn = {0378-3839}, doi = {10.1016/j.coastaleng.2004.10.003}, url = {Surf zone currents over irregular bathymetry were observed with GPS-tracked drifters and modeled with the depth-integrated nonlinear shallow water equations. Trajectories of drifters released in 1-2 m depth sometimes defined rip currents and surf zone eddies, features that have been difficult to resolve with fixed instruments. The drifter-delineated surf zone circulation evolved as the tidal level changed during each 4-6 hour deployment. In one case, as the tide dropped, a shore normal rip current present for the first 2 hours evolved to a more shore parallel flow. In a second case, on a rising tide a well-developed bifurcated rip current was replaced by a weak, amorphous circulation. Rip current velocities were strongest near the surf zone edge and decayed by an order of magnitude within 2 surf zone widths from the shoreline. An eddy was observed to persist over a bathymetric depression within the surf zone for at least 1 hour. Observed and numerically simulated drifter trajectories define similar flow features, but the observed and modeled velocities differed by roughly a factor of 2, and flow evolution observed during roughly 0.5 m changes in tidal level were reproduced only if the simulated water levels varied by about 1 m. The alongshore momentum balance was spatially variable, with wave forcing balanced by pressure gradient, friction, and advective terms. The cross-shore momentum balance was everywhere dominated by wave forcing and pressure gradient terms of about equal magnitude. In the vicinity of a simulated rip current the residual of the cross-shore wave forcing and pressure gradient increased and was balanced by advection terms.

}, keywords = {alongshore currents, barred beach, buoy, field, nearshore circulation, nonlinear shear instabilities, rip currents, swell, waves}, isbn = {0148-0227}, doi = {10.1029/2004jc002421}, url = {Alongshore propagating meanders of the mean alongshore current in the surf zone called shear waves have periods of a few minutes and wavelengths of a few hundred meters. Here shear wave properties are estimated with arrays of current meters deployed for 4 months within 300 m of the shoreline of a sandy beach. Shear wave velocity fluctuations are approximately horizontally isotropic, with root mean square values between 10 and 40\% of the mean (3-hour-averaged) alongshore current V. Cross-shore variations of the time-averaged shear wave momentum flux are consistent with shear wave energy generation close to shore where the breaking wave-driven mean alongshore current V and current shear V-x are strong and with shear wave energy dissipation and transfer back to the mean flow farther offshore where V and V-x are weak. In case studies where V is a narrow jet near the shoreline the observed strong decay of shear wave energy levels seaward of the jet, and the cross-shore and alongshore structure of shear waves within the jet, are similar to predictions based on the linearly unstable modes of the observed V. Shear wave energy levels also are high in a marginally unstable case with a strong, but weakly sheared, V.

}, keywords = {alongshore currents, beaches, directional spectra, frequency, instabilities, longshore currents, mean longshore-current, nearshore, shear waves, surf zone, variance}, isbn = {0148-0227}, doi = {10.1029/2002jc001761}, url = {[1] Vertical flow structure and turbulent dissipation in the swash zone are estimated using cross-shore fluid velocities observed on a low-sloped, fine-grained sandy beach [Raubenheimer, 2002] with two stacks of three current meters located about 2, 5, and 8 cm above the bed. The observations are consistent with an approximately logarithmic vertical decay of wave orbital velocities within 5 cm of the bed. The associated friction coefficients are similar in both the uprush and downrush, as in previous laboratory results. Turbulent dissipation rates estimated from velocity spectra increase with decreasing water depth from O(400 cm(2)/s(3)) in the inner surf zone to O(1000 cm(2)/s(3)) in the swash zone. Friction coefficients in the swash interior estimated with the logarithmic model and independently estimated by assuming that turbulent dissipation is balanced by production from vertical shear of the local mean flow and from wave breaking are between 0.02 and 0.06. These values are similar to the range of friction coefficients ( 0.02 - 0.05) recently estimated on impermeable, rough, nonerodible laboratory beaches and to the range of friction coefficients (0.01 - 0.03) previously estimated from field observations of the motion of the shoreward edge of the swash (run-up).

}, keywords = {beach, breaking waves, fields, height, profile, sediment transport, shear-stress, surf zone, swash, turbulence measurements, velocimetry, waves}, isbn = {0148-0227}, doi = {10.1029/2003jc001877}, url = {Inverse models are developed that use data and dynamics to estimate optimally the breaking-wave-driven setup and alongshore current, as well as the cross-shore forcing, alongshore forcing, and drag coefficient. The inverse models accurately reproduce these quantities in a synthetic barred-beach example. The method is applied to one case example each from the Duck94 and SandyDuck field experiments. Both inverse solutions pass consistency tests developed for the inverse method and have forcing corrections similar to a roller model and significant cross-shore variation of the drag coefficient. The inverse drag coefficient is related to the wave dissipation, a bulk measure of the turbulence source, but not to the bed roughness, consistent with the hypothesis that breaking- wave-generated turbulence increases the drag coefficient. Inverse solutions from a wider range of conditions are required to establish the generality of these results.

}, keywords = {barred beaches, breaking waves, evolution, field, longshore currents, roughness, shear instabilities, surf zone}, isbn = {0022-3670}, doi = {10.1175/1520-0485(2004)034<0920:imoosa>2.0.co;2}, url = {The bottom drag coefficient in the nearshore has been suggested to depend on bottom roughness (bedforms) or alternatively on wave breaking. The hypothesis that bottom drag coefficient depends on bottom roughness is tested with 2 months of field observations collected on a sandy ocean beach during the Duck94 field experiment. Both the drag coefficient (estimated from alongshore momentum balances) and bottom roughness (estimated from fixed altimeters) are larger within the surfzone than in the region farther seaward. Although the drag coefficient increases with roughness seaward of the surfzone, no relationship was found between the drag coefficient and roughness-related quantities within the surfzone. These results suggest that breaking-wave generated turbulence increases the surfzone drag coefficient. (C) 2003 Elsevier Science B.V. All rights reserved.

}, keywords = {bed roughness, circulation, drag coefficient, evolution, longshore-current, nearshore, obliquely incident, surf zone, turbulence}, isbn = {0378-3839}, doi = {10.1016/s0378-3839(03)00026-7}, url = {A drifter designed to measure surf zone circulation has been developed and field tested. Drifter positions accurate to within a few meters are estimated in real time at 0.1 Hz using the global positioning system (GPS) and a shore-to-drifter radio link. More accurate positions are estimated at 1 Hz from postprocessed, internally logged data. Mean alongshore currents estimated from trajectories of the 0.5-m-draft drifters in 1-2-m water depth agree well with measurements obtained with nearby, bottom-mounted, acoustic current meters. Drifters deployed near the base of a well-developed rip current often followed eddylike paths within the surf zone before being transported seaward.

}, keywords = {coastal, currents, nearshore circulation}, isbn = {0739-0572}, doi = {10.1175/1460.1}, url = {Nearshore circulation, observed for 4 months on a 200-m-long stretch of natural beach during the SandyDuck field experiment, is shown to be alongshore uniform. An alongshore momentum balance between (wind and wave) forcing and bottom stress, cross-shore integrated between the shoreline and approximately 4 m water depth, holds on each of five instrumented cross-shore transects (skillgreater than or equal to0.87). The corresponding five best fit drag coefficients are similar, consistent with the assumption that terms in the momentum balance associated with alongshore nonuniformity are negligible. In addition, the alongshore nonuniformity of the circulation and bathymetry were examined at five cross-shore locations. Except near the shoreline, the circulation and bathymetry were rarely strongly alongshore nonuniform, and the circulation nonuniformities were usually no larger than expected from current-meter noise alone. Near the shoreline, the bathymetry was more irregular and the circulation was often detectably nonuniform, although no relationship between bathymetric and circulation nonuniformities was found. The closure of the alongshore momentum balances on cross-shore transects, and the observed alongshore uniformity of the circulation on four of five alongshore transects, demonstrates that the simplified dynamics of alongshore uniform circulation are valid during the experiment.

}, keywords = {bathymetry, circulation, longshore currents, momentum balances, nearshore, ocean, Oceanography, SandyDuck, waves}, isbn = {0148-0227}, doi = {10.1029/2001jc001293}, url = {[1] A Boussinesq model for the nonlinear transformation of the frequency-directional spectrum and bispectrum of surface gravity waves propagating over a gently sloping, alongshore uniform beach is compared with field and laboratory observations. Outside the surf zone the model predicts the observed spectral evolution, including energy transfers to harmonic components traveling in the direction of the dominant waves, and the cross-interactions of waves traveling in different directions that transfer energy to components with the vector sum wavenumber. The sea surface elevation skewness and asymmetry, third-order moments believed to be important for sediment transport, also are predicted well. Effects of surf zone wave breaking are incorporated with a heuristic frequency-dependent dissipation term in the spectral energy balance equation and an empirical relaxation of the bispectrum to Gaussian statistics. The associated coefficients are calibrated with observations that span a wide range of surf zone conditions. With calibrated coefficients, the model predicts observed surf zone frequency spectra well and surf zone skewness and asymmetry fairly well. The observed directional spectra inside the surf zone are broader than the predicted spectra, suggesting that neglected scattering effects associated with the random onset of wave breaking or with higher-order nonlinearity may be important.

}, keywords = {beach, boussinesq model, breaking waves, energy, evolution, nearshore, ocean waves, surf, surface gravity-waves, water, wave spectra}, isbn = {0148-0227}, doi = {10.1029/2001jc001304}, url = {Low-salinity water from Chesapeake Bay forms an intermittent buoyant gravity current that propagates more than 100 km southward along the coast. During five events when wind and surface gravity-wave forcing were weak, the buoyant coastal current 90 km south of Chesapeake Bay was less than 5 km wide, was 5-10 m thick, and propagated alongshore at similar to50 cm s(-1). The density decreased 2-3 kg m(-3) over a few hundred meters at the nose of the buoyant coastal current, which was located about 1 km offshore in; 8 m of water. Water up to 4 km ahead of the advancing nose was displaced southward and offshore (maximum velocities near the nose of 20 and 10 cm s(-1), respectively). The southward alongshore current increased abruptly to similar to50 cm s(-1) at the nose and continued to increase to a supercritical maximum of similar to70 cm s(-1) about 1 km behind the nose. An onshore flow of between 5 and 15 cm s(-1), which extended at least 5 km behind the nose, supplied buoyant water to the onshore region of weak, subcritical alongshore flow. The observed flow structure is qualitatively similar to theoretical predictions and laboratory measurements of buoyant gravity currents propagating along a sloping bottom.

}, keywords = {bay outflow plume, chesapeake bay, continental-shelf, gravity current, momentum balances, new-jersey shelf, north-carolina shelf, river plume, rotating fluid, sloping bottom}, isbn = {0022-3670}, doi = {10.1175/1520-0485(2003)33<933:ootffn>2.0.co;2}, url = {[1] The variation of seaward and shoreward infragravity energy fluxes across the shoaling and surf zones of a gently sloping sandy beach is estimated from field observations and related to forcing by groups of sea and swell, dissipation, and shoreline reflection. Data from collocated pressure and velocity sensors deployed between 1 and 6 m water depth are combined, using the assumption of cross-shore propagation, to decompose the infragravity wave field into shoreward and seaward propagating components. Seaward of the surf zone, shoreward propagating infragravity waves are amplified by nonlinear interactions with groups of sea and swell, and the shoreward infragravity energy flux increases in the onshore direction. In the surf zone, nonlinear phase coupling between infragravity waves and groups of sea and swell decreases, as does the shoreward infragravity energy flux, consistent with the cessation of nonlinear forcing and the increased importance of infragravity wave dissipation. Seaward propagating infragravity waves are not phase coupled to incident wave groups, and their energy levels suggest strong infragravity wave reflection near the shoreline. The cross-shore variation of the seaward energy flux is weaker than that of the shoreward flux, resulting in cross-shore variation of the squared infragravity reflection coefficient (ratio of seaward to shoreward energy flux) between about 0.4 and 1.5.

}, keywords = {0.005-0.05 hz motions, beach, cross-shore evolution, edge waves, Energy flux, generation, infragravity waves, model, nonlinear phase coupling, shelf, shoreline reflection, surf zone, surface gravity-waves}, isbn = {0148-0227}, doi = {10.1029/2001jc000970}, url = {The nonlinear dispersion of random, directionally spread surface gravity waves in shallow water is examined with Boussinesq theory and field observations. A theoretical dispersion relationship giving a directionally averaged wavenumber magnitude as a function of frequency, the local water depth, and the local wave spectrum and bispectrum is derived for waves propagating over a gently sloping beach with straight and parallel depth contours. The linear, nondispersive shallow water relation is recovered as the first-order solution, with weak frequency and amplitude dispersion appearing as second-order corrections. Wavenumbers were estimated using four arrays of pressure sensors deployed in 2-6-m depth on a gently sloping sandy beach. When wave energy is low, the observed wavenumbers agree with the linear, finite-depth dispersion relation over a wide frequency range. In high energy conditions, the observed wavenumbers deviate from the linear dispersion relation by as much as 20\%-30\% in the frequency range from two to three times the frequency of the primary spectral peak, but agree well with the nonlinear Boussinesq dispersion relation, confirming that the deviations from linear theory are finite amplitude effects. In high energy conditions, the predicted frequency and amplitude dispersion tend to cancel, yielding a nearly nondispersive wave field in which waves of all frequencies travel with approximately the linear shallow water wave speed, consistent with the observations. The nonlinear Boussinesq theory wavenumber predictions (based on the assumption of irrotational wave motion) are accurate even within the surf zone, suggesting that wave breaking on gently sloping beaches has little effect on the dispersion relation.

}, keywords = {beach, boussinesq equations, breaking waves, depth, directional spectra, evolution, field, model, natural}, isbn = {0022-3670}, doi = {10.1175/1520-0485(2002)032<1181:ndosgw>2.0.co;2}, url = {Shear waves (instabilities of the breaking wave-driven mean alongshore current) and gravity waves both contribute substantial velocity fluctuations to nearshore infragravity motions (periods of a few minutes). Three existing methods of estimating the shear wave contribution to the infragravity velocity variance are compared using extensive field observations. The iterative maximum likelihood estimator (IMLE) and the direct estimator (DE) methods use an alongshore array of current meters, and ascribe all the velocity variance at non-gravity wavenumbers to shear waves. The ratio (R) method uses a collocated pressure gauge and current meter, and assumes that shear wave pressure fluctuations are small, and that the kinetic and potential energies of gravity waves are equal. The shear wave velocity variance [q(sw)(2)] estimated from the relative magnitudes of the total (shear plus gravity wave) pressure and velocity variances. Estimates of root-mean-square shear wave velocity fluctuations root [q(sw)(2)] from all three methods are generally in good agreement (correlations \>0.96), supporting the validity of their underlying assumptions. When root [q(sw)(2)] is greater than a few centimeters per second, IMLE and DE estimates of root [q(sw)(2)] differ by less than 10\%. The R estimates of root [q(sw)(2)] are usually higher than the IMLE and DE estimates, and on average the R method attributes 15\% more of the total horizontal velocity variance to shear waves than is attributed by the IMLE method. When mean currents and shear waves are weak, all three estimators are noisy and biased high.

}, keywords = {beach, gravity, instabilities, mean longshore-current}, isbn = {0739-0572}, doi = {10.1175/1520-0426(2002)019<0136:comfen>2.0.co;2}, url = {Mean alongshore currents observed on two barred beaches are compared with predictions based on the one-dimensional, time- and depth-averaged alongshore momentum balance between forcing (by breaking waves, wind, and 10-100 km scale alongshore surface slopes), bottom stress, and lateral mixing. The observations span 500 hours at Egmond, Netherlands, and 1000 hours at buck, North Carolina, and include a wide range of conditions with maximum mean currents of 1.4 m/s. Including rollers in the wave forcing results in improved predictions of the observed alongshore-current structure by shifting the predicted velocity maxima shoreward and increasing the velocity in the bar trough compared with model predictions without rollers. For these data, wave forcing balances the bottom stress within the surfzone, with the other terms of secondary importance. The good agreement between observations and predictions implies that the one-dimensional assumption holds for the range of conditions examined, despite the presence of small alongshore bathymetric nonuniformities. With stronger bathymetric variations the model skill deteriorates, particularly in the bar trough, consistent with earlier modeling and laboratory studies.

}, keywords = {breaking waves, evolution, longshore currents, momentum balances, nearshore, surf zone}, isbn = {0148-0227}, doi = {10.1029/2000jc000766}, url = {Wave-driven setdown and setup observed for 3 months on a cross-shore transect between the shoreline and 5 m water depth on a barred beach are compared with a theoretical balance between cross-shore gradients of the mean water level and the wave radiation stress. The observed setdown, the depression of the mean water level seaward of the surf zone, is predicted well when radiation stress gradients are estimated from the observations using linear theory at each location along the transect. The observed setdown also agrees with analytical predictions based on offshore wave observations and the assumption of linear, dissipationless, normally incident waves shoaling on alongshore homogeneous bathymetry. The observed setup, the superelevation of the mean water level owing to wave breaking, is predicted accurately in the outer and middle surf zone, but is increasingly underpredicted as the shoreline is approached. Similar to previous field studies, setup at a fixed cross-shore location increases with increasing offshore wave height and is sensitive to tidal fluctuations in the local water depth and to bathymetric changes. Numerical simulations and the observations suggest that setup near the shoreline depends on the bathymetry of the entire surf zone and increases with decreasing surf zone beach slope, defined as the ratio of the surf zone-averaged water depth to the surf zone width. A new empirical formula for shoreline setup on nonplanar beaches incorporates this dependence.

}, keywords = {breaking, heights, model, natural beach, surf zone, swash, transformation, water}, isbn = {0148-0227}, doi = {10.1029/2000jc000572}, url = {Field observations suggest that onshore sandbar migration, observed when breaking-wave-driven mean flows are weak, may be related to the skewed fluid accelerations associated with the orbital velocities of nonlinear surface waves. Large accelerations (both increases and decreases in velocity magnitudes), previously suggested to increase sediment suspension, occur under the steep wave faces that immediately precede the maximum onshore-directed orbital velocities. Weaker accelerations occur under the gently sloping rear wave faces that precede the maximum offshore-directed velocities. The timing of strong accelerations relative to onshore flow is hypothesized to produce net onshore sediment transport. The observed acceleration skewness, a measure of the difference in the magnitudes of accelerations under the front and rear wave faces, is maximum near the sandbar crest. The corresponding cross-shore gradients of an acceleration-related onshore sediment transport would cause erosion offshore and accretion onshore of the bar crest, consistent with the observed onshore migration of the bar crest. Furthermore, the observations and numerical simulations of nonlinear shallow water waves show that the region of strongly skewed accelerations moves shoreward with the bar, suggesting that feedback between waves and evolving morphology can result in continuing onshore bar migration.

}, keywords = {beach, bispectra, evolution, sediment transport model, surface gravity-waves, suspension}, isbn = {0148-0227}, doi = {10.1029/2000jc000389}, url = {Alongshore gradients in wave energy and propagation direction were observed near a pier that extends 500 m from the Duck, N.C., shoreline to about 6-m water depth. When incident waves approached the beach obliquely, wave energy observed near the shoreline 200 m downwave of the pier was as much as 50\% lower than observed 400 m downwave, and waves close to the pier were mon normally incident than those farther downwave. Alongshore gradients were much smaller 400 m offshore of the shoreline, upwave of the pier and with nearly normally incident waves, confirming that the gradients are associated with wave propagation under the pier. A spectral refraction model for waves propagating over the measured bathymetry, which includes a depression under the pier, accurately predicts the observations 400 m downwave of the pier, but overpredicts energy near the pier. Refraction model predictions that include partial absorption of wave energy by the pier pilings reproduce the observed alongshore gradients, suggesting that piling-induced dissipation may be important.

}, keywords = {diffraction, pit}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(2001)127:1(2)}, url = {Statistics of the nearshore velocity field in the wind-wave frequency band estimated from acoustic Doppler, acoustic travel time, and electromagnetic current meters are similar. Specifically, current meters deployed 25-100 cm above the seafloor in 75-275-cm water depth in conditions that ranged from small-amplitude unbroken waves to bores in the inner surf zone produced similar estimates of cross-shore velocity spectra, total horizontal and vertical velocity variance, mean currents, mean wave direction, directional spread, and cross-shore velocity skewness and asymmetry. Estimates of seafloor location made with the acoustic Doppler sensors and collocated sonar altimeters differed by less than 5 cm. Deviations from linear theory in the observed relationship between pressure and velocity fluctuations increased with increasing ratio of wave height to water depth. The observed covariance between horizontal and vertical orbital velocities also increased with increasing height to depth ratio, consistent with a vertical flux of cross-shore momentum associated with wave dissipation in the surf zone.

}, keywords = {doppler current profiler, Sonar, waves}, isbn = {0739-0572}, doi = {10.1175/1520-0426(2001)018<1735:cmpits>2.0.co;2}, url = {The time-averaged alongshore bottom stress is an important component of nearshore circulation models. In a widely accepted formulation the bottom stress is proportional to \< \(u) over right arrow\v \>, the time average of the product of the instantaneous velocity magnitude \(u) over right arrow\ and the instantaneous alongshore velocity component v. Both mean and fluctuating (owing to random, directionally spread waves) velocities contribute to \< \(u) over right arrow\v \> Direct estimation of \< \(u) over right arrow\v \> requires a more detailed specification of the velocity field than is usually available, so the term \< \(u) over right arrow\v \> is parameterized. Here direct estimates of \< \(u) over right arrow\v \> based on time series of near-bottom currents observed between the shoreline and 8-m water depth are used to test the accuracy of \< \(u) over right arrow\v \> parameterizations. Common \< \(u) over right arrow\v \> parameterizations that are linear in the mean alongshore current significantly underestimate \< \(u) over right arrow\v \> for moderately strong alongshore currents, resulting in overestimation of a drag coefficient determined by fitting modeled (with a linearized bottom stress) to observed alongshore currents. A parameterization based on a joint-Gaussian velocity field with the observed velocity statistics gives excellent overall agreement with the directly estimated \< \(u) over right arrow\v \> and allows analytic investigation of the statistical properties of the velocity field that govern \< \(u) over right arrow\v \> Except for the weakest flows, \< \(u) over right arrow\v \> depends strongly on the mean alongshore current and the total velocity variance but depends only weakly on the mean wave angle, wave directional spread, and mean cross-shore current. Several other nonlinear parameterizations of \< \(u) over right arrow\v \> are shown to be more accurate than the linear parameterizations and are adequate for many modeling purposes.

}, keywords = {beaches, data, field, longshore currents, model, nearshore, nonlinear shear instabilities, surf-zone, transformation, waves}, isbn = {0148-0227}, doi = {10.1029/2000jc900022}, url = {We derive a general linear, weakly dispersive, Boussinesq-type equation that can be used to study edge waves on beaches with slow cross-shore variation of the depth and the alongshore current. The equation is more accurate than the non-dispersive shallow water equations and simpler than the fully dispersive elliptic mild slope equation (especially for a non-zero alongshore current). The improved performance of the new Boussinesq-type model is demonstrated using analytic solutions for edge waves on a plane beach with zero alongshore current. (C) 1999 Elsevier Science B.V. All rights reserved.

}, keywords = {boussinesq model, edge waves, mild slope model, weak dispersion}, isbn = {0378-3839}, doi = {10.1016/s0378-3839(99)00022-8}, url = {The resonant scattering of low-mode progressive edge waves by small-amplitude longshore periodic depth perturbations superposed on a plane beach has recently been investigated using the shallow water equations (Chen \& Guza 1998). Coupled evolution equations describing the variations of edge wave amplitudes over a finite-size patch of undulating bathymetry were developed. Here similar evolution equations are derived using the full linear equations, removing the shallow water restriction of small (2N + 1)theta, where N is the maximum mode number considered and theta is the unperturbed planar beach slope angle. The present results confirm the shallow water solutions for vanishingly small (2N + 1)theta and allow simple corrections to the shallow water results for small but finite (2N + 1)theta. Additionally, multi-wave scattering cases occurring only when (2N + 1)theta = O(1) are identified, and detailed descriptions are given for the case involving modes 0, 1, and 2 that occurs only on a steep beach with theta = pi/12.

}, isbn = {0022-1120}, doi = {10.1017/s0022112099004528}, url = {Four months of moored current, pressure, temperature, conductivity, wave, and wind observations on the North Carolina shelf indicate three dynamically distinct regions: the surf zone, the inner shelf between the surf zone and the 13-m isobath, and the midshelf, In the surf zone the along-shelf momentum balance is between the cross-shelf gradient of the wave radiation stress and the bottom stress. The linear drag coefficient in the surf zone is about 10 times larger than seaward of the surf zone. On the inner shelf the along-shelf momentum balance is also frictional; the along-shelf wind stress and pressure gradient are balanced by bottom stress. In the cross-shelf momentum balance the pressure gradient is the superposition of roughly equal contributions from the Coriolis force (geostrophy) and wave setdown from shoaling, unbroken surface gravity waves. At midshelf the along-shelf momentum balance is less frictional and hence flow accelerations are important. The cross-shelf momentum balance is predominantly geostrophic because the greater depth and smaller bottom slope at midshelf reduce the importance of wave setdown. The cross-shelf density gradient is in thermal wind balance with the vertical shear in the along-shelf flow in depths as shallow as 10 m. The dominant along-shelf momentum balances provide a simple estimate of the depth-averaged, along-shelf current in terms of the measured forcing (i.e., wind stress, wave radiation stress divergence, and along-shelf pressure gradient) that reproduces accurately the observed cross-shelf variation of the depth-averaged, along-shelf current between the surf zone and midshelf.

}, keywords = {california continental-shelf, dynamics, longshore currents, middle atlantic bight, model, nearshore, variability, waves, wind, winter}, isbn = {0148-0227}, doi = {10.1029/1999jc900101}, url = {Tidal water table fluctuations observed for 27 days in a gently sloped ocean beach are predicted well by numerical models based on the Boussinesq equation driven with the observed 10 min-averaged shoreline (ocean-beach intersection) motion. Diurnal and semidiurnal water table fluctuations are almost completely damped 100 m landward of the mean shoreline location on this fine-grained sand beach, but fluctuations at spring-neap periods (approximate to 14 days) are attenuated less. Comparison of the observations with the predictions suggests that the asymmetries in the water table level time series measured in this study result from nonlinearity owing to the large (relative to the wavelength) horizontal shoreline excursions, rather than from nonlinearity owing to finite-amplitude water table fluctuations. Cross-shore variations of the aquifer depth are predicted to have a small effect on the landward decay rate of the water table fluctuations. The seepage face width is predicted accurately and depends on the nonplanar beach profile. In general, the development of a seepage face is predicted to have little effect on the water table level landward of the intertidal region.

}, keywords = {dynamics, model, slug test, swash zone, waves}, isbn = {0043-1397}, doi = {10.1029/1999wr900105}, url = {Observations of surface gravity waves shoaling between 8-m water depth and the shoreline on a barred beach indicate that breaking results in an increase in the directional spread of wave energy, in contrast to the directional narrowing with decreasing depth predicted by refraction theory (Snell{\textquoteright}s law). During low-energy wave conditions, when breaking-induced wave energy losses over the instrumented transect are small, the observed mean propagation direction and spread about the mean both decrease with decreasing depth, consistent with the expected effects of refraction. Nonlinearity causes high-frequency components of the spectrum to become directionally aligned with the dominant incident waves. During high-energy wave conditions with significant wave breaking on the sand bar, the observed mean directions still decrease with decreasing depth. However, the observed directional spreads increase sharply (nominally a factor of 2 for values integrated over the swell-sea frequency range) between the outer edge of the surf zone and the crest of the sand bar, followed by a decrease toward the shoreline. Observations on a nonbarred beach also show directional broadening, with spreads increasing monotonically from the outer edge of the surf zone to a maximum value near the shoreline. Although the mechanism is not understood, these spatial patterns of directional broadening suggest that wave breaking causes significant scattering of incident wave energy into obliquely propagating components.

}, keywords = {beach, buoy, spectra, surface gravity-waves}, isbn = {0148-0227}, doi = {10.1029/1998jc900092}, url = {Comparison of predicted with observed attenuation of pressure fluctuations shows that wave heights can be estimated with observations from a pressure sensor that is buried a known depth in fine sand. The attenuation of pressure fluctuations within the sand bed under unbroken shoaling waves, bores in the surf zone, and swash near the shoreline was measured with vertical stacks of buried pressure sensors. The attenuation increased with increasing frequency and depth below the bed surface, consistent with previous observations under nonbreaking waves in deeper water and with model predictions based on pore-elastic theory, in the limit of an infinitely deep soil skeleton that is much more compressible than the pore fluid, the predicted pressure fluctuations decrease exponentially with increasing burial depth, and the attenuation is independent of the sediment properties. For the fine-grained sand beds considered here, this exponential limit accurately predicts the observed attenuation.

}, keywords = {water-waves}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1998)124:3(151)}, url = {The one-dimensional, time-averaged (over many wave periods) alongshore momentum balance between forcing by wind and breaking waves and the bottom stress is examined with field observations spanning a wide range of conditions on a barred beach. Near-bottom horizontal currents were measured for 2 months at 15 locations along a cross-shore transect extending 750 m from the shoreline to 8-m water depth. The hourly averaged bottom stress was estimated from observed currents using a quadratic drag law. The wave radiation stress was estimated in 8-m depth from an array of pressure sensors, and the wind stress was estimated from an anemometer at the seaward end of a nearby pier. The combined wind and wave forcing integrated ever the entire cross-shore transect is balanced by the integrated bottom stress. The wind stress contributes about one third of the forcing over the transect. Analysis of the momentum balances in different cross-shore regions shows that in the surf zone, wave forcing is much larger than wind forcing and that the bottom drag coefficient is larger in the surf zone than farther seaward, consistent with earlier studies.

}, keywords = {beach, breaking, longshore currents, ocean, shear-stress, surf zone, waves, wind}, doi = {10.1029/98jc01270}, url = {Waves, currents, and the location of the seafloor were measured on a barred beach for about 2 months at nine locations along a cross-shore transect extending 255 m from 1 to 4 m water depth. The seafloor location was measured nearly continuously, even in the surf zone during storms, with sonar altimeters mounted on fixed frames. The crest of a sand bar initially located about 60 m from the shoreline moved 130 m offshore (primarily when the offshore significant wave height exceeded about 2 m), with 1.5 m of erosion near the initial location and I m of accretion at the final location. An energetics-type sediment transport model driven by locally measured near-bottom currents predicts the observed offshore bar migration, but not the slow onshore migration observed during low-energy wave conditions. The predicted offshore bar migration is driven primarily by cross-shore gradients in predicted suspended sediment transport associated with quasi-steady, near-bottom, offshore flows. These strong (\> 50 cm/s) currents, intensified near the bar crest by wave breaking, are predicted to cause erosion on the shoreward slope of the bar and deposition on the seaward side. The feedback amoung morphology, waves, circulation, and sediment transport thus forces offshore bar migration during storms.

}, keywords = {cross-shore currents, environment, generation, model, nearshore, plane sloping beach, sediment transport, surf-zone}, doi = {10.1029/97jc02765}, url = {The resonant scattering of topographically trapped, low-mode progressive edge waves by longshore periodic topography is investigated using a multiple-scale expansion of the linear shallow water equations. Coupled evolution equations for the slowly varying amplitudes of incident and scattered edge waves are derived for small-amplitude, periodic depth perturbations superposed on a plane beach. In {\textquoteright}single-wave scattering{\textquoteright}, an incident edge wave is resonantly scattered into a single additional progressive edge wave having the same or different mode number (i.e. longshore wavenumber), and propagating in the same or opposite direction (forward and backward scattering, respectively), as the incident edge wave. Backscattering into the same mode number as the incident edge wave, the analogue of Brgg Scattering of surface waves, is a special case. In {\textquoteright}multi-wave scattering{\textquoteright}, simultaneous forward and backward resonant scattering results in several (rather than only one) new progressive edge waves. Analytic solutions are obtained for single-wave scattering and for a special case of multi-wave scattering involving mode-0 and mode-1 edge waves, over perturbed depth regions of both finite and semi-infinite longshore extent. In single-wave backscattering with small (subcritical) detuning (i.e. departure from exact resonance), the incident and backscattered wave amplitudes both decay exponentially with propagation distance over the periodic bathymetry, whereas with large (supercritical) detuning the amplitudes oscillate with distance. In single-wave forward scattering, the wave amplitudes are oscillatory regardless of the magnitude of the detuning. Multiwave solutions combine aspects of single-wave backward and forward scattering. In both single- and multi-wave scattering, the exponential decay rates and oscillatory wavenumbers of the edge wave amplitudes depend on the detuning. The results suggest that naturally occurring rhythmic features such as beach cusps and crescentic bars are sometimes of large enough amplitude to scatter a significant amount of incident low-mode edge wave energy in a relatively short distance (O(10) topographic wavelengths).

}, keywords = {bars, beds, bragg reflection, sandbars, surface-waves}, isbn = {0022-1120}, url = {Inverse methods are used to assimilate wave observations into numerical predictions of ocean swell (0.04-0.12 Hz surface waves) propagating over complex continental shelf bathymetry. Model predictions of swell on the shelf can be degraded by the limited accuracy and resolution of the initializing offshore (unsheltered deep water) frequency-directional spectra S-o, usually derived from buoy measurements or meteorological hindcasts. The authors use a spectral refraction wave propagation model to find improved estimates of S-o that are consistent with both unsheltered and sheltered (altered by coastal bathymetry) observations, and vary smoothly in direction and time. In Part I, linear and nonlinear inverse assimilation methods are developed. Their potential and limitations are illustrated qualitatively using a scenario where no a priori knowledge of S-o is used in the inverse estimates. Inverse estimates of S-o based solely on sheltered wave data routinely collected in the Southern California Eight are compared to meteorological hindcasts of peak offshore swell directions for two time periods dominated by swell arrivals from a distant storm. Robust model-hindcast agreement for the peak direction of an energetic, unimodal North Pacific swell event demonstrates that offshore directional information can be inferred solely from sheltered measurements. The poor model-hindcast agreement for a south swell event is markedly improved by the a priori assumption that S-o is unimodal with a prescribed parametric form, but assumptions about the shape of S-o severely reduce the generality of the approach. The authors conclude that conventional (low directional resolution) measurements from a few sheltered sites cannot be used to routinely resolve S-o, and offshore measurements for hindcasts of S-o are needed as additional constraints in practical applications. In Part II, the inverse methods are generalized to include hindcasts or unsheltered directional buoy data as primary constraints and sheltered observations are used to enhance the directional resolution and stability of S-o. Initialized with these S-o, the wave model yields improved predictions of regional swell conditions. The value of assimilating coastal observations into regional wave predictions is demonstrated with a comprehensive field study.

}, keywords = {directional spectra, models}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1998)028<0679:acwoir>2.0.co;2}, url = {Predictions from Boussinesq-equation-based models for the evolution of breaking surface gravity waves in shallow water are compared with field and laboratory observations. In the majority of the 10 cases investigated, the observed spectral evolution across the surf zone is modeled more accurately by a dissipation that increases at high frequency than by a frequency-independent dissipation. However, in each case the predicted spectra are qualitatively accurate for a wide range of frequency-dependent dissipations, apparently because preferential reduction of high-frequency energy (by dissipation that increases with increasing frequency) is largely compensated by increased nonlinear energy transfers to high frequencies. In contrast to the insensitivity of predicted spectral levels, model predictions of skewness and asymmetry (statistical measures of the wave shapes) are sensitive to the frequency dependence of the dissipation. The observed spatial evolution of skewness and asymmetry is predicted qualitatively well by the model with frequency-dependent dissipation, but ij predicted poorly with frequency-independent dissipation. Although the extension of the Boussinesq equations to breaking waves is ad hoc, a dissipation depending on the frequency squared (as previously suggested) reproduces well the observed evolution of wave frequency spectra, skewness, and asymmetry.

}, keywords = {beach, bispectra, boussinesq equations, gravity-waves, predictions, propagation, run-up, swash, transformation}, doi = {10.1029/97jc01565}, url = {A technique to simulate non-Gaussian time series with a desired ({\textquoteright}{\textquoteright}target{\textquoteright}{\textquoteright}) power spectrum and bispectrum is applied to ocean waves. The targets were obtained from observed bottom pressure fluctuations of shoaling, nonbreaking waves in 2-9 m water depth. The variance (i.e., frequency integrated spectrum), skewness, and asymmetry (i.e., frequency integrated bispectrum) of the simulated time series compare favorably with the observations, even for highly skewed and asymmetric near-breaking waves. The mean lengths of groups of high waves from non-Gaussian simulated time series are closer to observed values than those from Gaussian simulations. The simulations suggest that quadratic phase coupling between waves (of different frequencies) in shallow water results in longer wave groups than occur with linear, uncoupled waves having the identical power spectrum.

}, keywords = {gravity-waves, linear-theory}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1997)123:2(68)}, url = {Field observations and numerical model predictions are used to investigate the effects of nonlinear interactions, reflection, and dissipation on the evolution of surface gravity waves propagating across a barred beach. Nonlinear interactions resulted in a doubling of the number of wave crests when moderately energetic (about 0.8-m significant wave height), narrowband swell propagated without breaking across an 80-m-wide, nearly flat (2-m depth) section of beach between a small offshore sand bar and a steep (slope = 0.1) beach face, where the waves finally broke. These nonlinear energy transfers are accurately predicted by a model based on the nondissipative, unidirectional (i.e., reflection is. neglected) Boussinesq equations. For a lower-energy (wave height about 0.4 m) bimodal wave field, high-frequency seas dissipated in the surf zone; but lower-frequency swell partially reflected from the steep beach face, resulting in significant cross-shore modulation of swell energy. The combined effects of reflection from the beach face and dissipation across the sand bar and near the shoreline are described well by a bore propagation model based on the nondispersive nonlinear shallow water equations. Boussinesq model predictions on the flat section (where dissipation is weak) are improved by decomposing the wave field into seaward and shoreward propagating components. In more energetic (wave heights greater than 1 m) conditions, reflection is negligible, and the region of significant dissipation can extend well seaward of the sand bar. Differences between observed decreases in spectral levels and Boussinesq model predictions of nonlinear energy transfers are used to infer the spectrum pf breaking wave induced dissipation between adjacent measurement locations. The inferred dissipation rates typically increase with increasing frequency and are comparable in magnitude to the nonlinear energy transfer rates.

}, keywords = {model, surface gravity-waves, transformation}, doi = {10.1029/97jc01010}, url = {Extensive field observations are used to characterize seiches (periods 0.5-30 min) in three small harbors with similar surface areas (similar to 1 km(2)), water depths (5-12 m), and swell wave climates. On the continental shelf just offshore of each harbor mouth, the energy levels of waves in the infragravity frequency band 0.002-0.03 Hz (periods 0.5-10 min) vary by more than a factor of 200 in response to comparably large variations in swell energy levels. Energy levels in this swell-driven frequency band also vary (less dramatically) in response to changes in the swell frequency and with tidal stage. Motions at longer seiche periods (10-30 min) are primarily driven by meteorological and other processes (a tsunami-generated seiche is described). As has often been observed, the amplification of seiche energy within each harbor basin (relative to energy in the same frequency band outside the harbor) varies as a function of seiche frequency, and is largest at the frequency of the lowest resonant harbor mode (i.e., the Helmholtz or grave mode). At all three harbors, the average amplification of the grave mode decreases (by at least a factor of 2) with increasing seiche energy, a trend consistent with a nonlinear dissipation mechanism such as flow separation in the harbor mouth or sidewall and bottom friction.

}, keywords = {0.005-0.05 hz motions, coast, infragravity waves, large-amplitude, shelf}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1996)122:5(232)}, url = {For a significant range of offshore wave conditions and foreshore slopes, run-up observations are compared to semiempirical formulations and predictions of an existing numerical model based on the depth-averaged one-dimensional nonlinear shallow water equations with bore-like breaking wave dissipation and quadratic bottom friction. The numerical model is initialized with time series of sea surface elevation and cross-shore velocity observed in 80 cm mean water depth (approximately 50 m offshore of the mean shoreline) on a gently sloping beach and in 175 cm water depth (100 m offshore of the shoreline) on a steep concave beach. Run-up was measured with a stack of resistance wires at elevations 5, 10, 15, 20, and 25 cm above and parallel to the beach face. At sea swell frequencies (nominally 0.05 \< f less than or equal to 0.18 Hz), run-up energy is limited by surf zone dissipation of shoreward propagating waves so that increasing the offshore wave height above a threshold value does not substantially increase the predicted or observed sea swell run-up excursions (e.g., run-up is {\textquoteright}{\textquoteright}saturated{\textquoteright}{\textquoteright}). Existing semiempirical saturation formulations are most consistent with the observations and numerical model predictions of run-up excursions nearest the bed. In contrast, at infragravity frequencies (0.004 \< f less than or equal to 0.05 Hz) where surf zone dissipation is relatively weak and reflection from the beach face is strong (e.g., saturation formulas are not applicable), the run-up excursions increase approximately linearly with increasing offshore wave height. The numerical model also accurately predicts that the tongue-like shape of the run-up results in sensitivity of run-up measurements to wire elevation. For instance, run-up excursions and mean vertical superelevation (above the offshore still water level) increase with decreasing wire elevation, and continuous thinning of the run-up tongue during the wave uprush can result in large phase differences between run-up excursions measured at different wire elevations. Numerical model simulations suggest that run-up measured more than a few centimeters above the bed cannot be used to infer even the sign of the fluid velocities in the run-up tongue.

}, keywords = {bore, natural beach, setup, slopes, surf, swash, wave reflection}, isbn = {0148-0227}, doi = {10.1029/96jc02432}, url = {Sea and swell wave heights observed on transects crossing the mid and inner surf zone on three beaches (a steep concave-up beach, a gently sloped approximately planar beach, and a beach with an approximately flat terrace adjacent to a steep foreshore) were depth limited (i.e., approximately independent of the offshore wave height), consistent with previous observations. The wave evolution is well predicted by a numerical model based on the one-dimensional nonlinear shallow water equations with bore dissipation. The model is initialized with the time series of sea surface elevation and cross-shore current observed at the most offshore sensors (located about 50 to 120 m from the mean shoreline in mean water depths 0.80 to 2.10 m). The model accurately predicts the cross-shore variation of energy at both infragravity (nominally 0.004 \< f less than or equal to 0.05 Hz),nd sea swell (here 0.05 \< f less than or equal to 0.18 Hz) frequencies. In models of surf zone hydrodynamics, wave-energy dissipation is frequently parameterized in terms of gamma(s), the ratio of the sea swell significant wave height to the local mean water depth. The observed and predicted values of gamma(s) increase with increasing beach slope beta and decreasing normalized (by a characteristic wavenumber k) water depth kh and are well correlated with beta/kh, a measure of the fractional change in water depth over a wavelength. Errors in the predicted individual values of gamma(s) are typically less than 20\%. It has been suggested that infragravity motions affect waves in the sea swell band and hence gamma(s), but this speculation is difficult to test with field observations. Numerical simulations suggest that for the range of conditions considered here, gamma(s) is insensitive to infragravity energy levels.

}, keywords = {decay, energy, height, incident sea waves, model, natural beach, random breaking waves, run-up, saturation, swash, water}, isbn = {0148-0227}, doi = {10.1029/96jc02433}, url = {The performance of the Datawell Directional Waverider and the National Data Buoy Center.(NDBC) 3-m discus buoy, widely used to measure the directional properties of surface gravity waves, are evaluated through comparisons to an array of six pressure transducers mounted 14 m below the sea surface on a platform in 200-m depth, Each buoy was deployed for several months within a few kilometers of the platform. The accuracy of the platform ground-truth army was verified by close agreement of wavenumber estimates with the theoretical linear dispersion relation for surface gravity waves. Buoy and army estimates of wave energy and directional parameters, based on integration of the directional moments across{\textquoteright} the frequency band of energetic swell (0.06-0.14 Hz), are compared for a wide range of wave conditions. Wave energy and mean propagation direction estimates from both buoys agree well with the platform results. However, the Datawell buoy provides significantly better estimates of directional spread and skewness than the NDBC buoy.

}, keywords = {field-evaluation, wave}, isbn = {0739-0572}, doi = {10.1175/1520-0426(1996)013<0231:acodba>2.0.co;2}, url = {A 1 MHz sonar altimeter with automatic gain control is shown to provide accurate estimates of the distance between the instrument and the seafloor. Laboratory experiments indicate that distance estimates degrade slightly when the bottom is rough or sloped and when sediment is suspended in the water column. Results from field tests, both within and seaward of the surf zone, show some degradation owing to a combination of suspended sediment and bubbles, bed undulations, and perhaps the dynamic nature of the sand bottom under waves. Seaward of the surf zone the bottom can be located within +/2 cm nearly continuously, whereas inside the surf zone the bottom can be located only intermittently and the accuracy decreases to +/3 cm. A 300 m long cross-shore transect of 16 altimeters was deployed from the shoreline to about 4 m depth for 3 months in summer-fall 1994 near Duck, NC. Results show that the altimeters are robust and can usually provide estimates of the seafloor position every few minutes even in the surf zone during large storms.

}, isbn = {0025-3227}, doi = {10.1016/0025-3227(96)00018-7}, url = {Waves observed in the inner surf and swash zones of a fine grained, gently sloping beach are modeled accurately with the nonlinear shallow water equations. The model is initialized with observations from pressure and current sensors collocated about 50 m from the mean shoreline in about 1 m depth, and model predictions are compared to pressure fluctuations measured at five shoreward locations and to run-up. Run-up was measured with a vertical stack of five wires supported parallel to and above the beach face at elevations of 5, 10, 15, 20, and 25 cm. Each 60-m-long run-up wire yields time series of the most shoreward location where the water depth exceeds the wire elevation. As noted previously, run-up measurements are sensitive to the wire elevation owing to thin run-up tongues not measured by the more elevated wires. As the wire elevation increases, the measured mean run-up location moves seaward, low-frequency (infragravity) energy decreases, and higher-frequency sea swell energy increases. These trends, as well as the variation of wave spectra and shapes (e.g., wave skewness) across the inner surf zone, are well predicted by the numerical model.

}, keywords = {gravity-waves, model, moments, natural beach, run-up, setup, slopes, surf beat}, isbn = {0148-0227}, doi = {10.1029/95jc00232}, url = {The effect of a Macrocystis kelp forest on shoreward propagating surface gravity waves was measured. Observations were made over a 67-day period at four locations around a 350-m-wide kelp bed off Carlsbad, California. Instruments were located directly offshore and onshore of the kelp bed at depths of 13 m and 8 m, respectively, and at control stations at the same depths, but displaced 750 m alongshore, away from the kelp bed. The bathymetry between the offshore and onshore sites was gently sloping and featureless. The measured spectra, significant wave height, mean wave direction at peak frequency, and total radiation stress differed only slightly between the offshore kelp and control stations and were similar at the onshore sites. The similarity of the wave field at the onshore kelp and control sites shows that this typical southern California kelp bed, with an average density of about 10 plants per 100 m(2), does not have a significant effect on waves. These measurements can be used to place upper bounds on drag coefficients in numerical models of the effect of kelp on waves.

}, keywords = {energy, spectra}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1995)121:2(143)}, url = {Bispectral and trispectral analyses are used to detect secondary and tertiary wave components resulting from nonlinear interactions among large-amplitude ocean surface gravity waves in 8- and 13-m water depths. Bispectra of bottom-pressure measurements indicate forced secondary waves at frequencies 2f(p) about twice the primary power spectral peak frequency f(p). However, the interpretation of the bispectrum at sum frequencies of approximately 3f(p) is ambiguous because contributions of both secondary and tertiary forced waves may be significant. Trispectral analysis confirms the presence of tertiary waves with frequency approximately 3f(p) In 8 m depth the tertiary bottom-pressure field is dominated by interactions between three colinearly propagating wind-wave components with frequencies close to f(p). In 13 m depth these relatively short-wavelength forced waves are strongly attenuated at the seafloor and the tertiary wave field is driven by interactions between the dominant waves at f(p) and obliquely propagating higher-frequency wind waves. The phases of the higher-order spectra are consistent with weakly nonlinear wave theory (Hasselmann, 1962).

}, keywords = {bispectra, statistics}, isbn = {0148-0227}, doi = {10.1029/94jc02900}, url = {Runup kinematics on a gently sloping natural beach are examined with detailed measurements from video images, resistance wires deployed at five elevations (between 5 and 25 cm) above and parallel to the beach face, and pressure sensors located in the inner surf zone. As suggested in a previous study comparing a single-level resistance wire and manually digitized films, runup measurements are sensitive to the sensor elevation above the bed, owing to the elongated shape of the runup tongue. The measured mean runup elevation (setup) and vertical excursion increase as the sensor elevation decreases, with the video-based runup estimates having the maximum means and variances. For the six data runs the average ratios of the video-based setup and significant runup excursion to estimates based on wires elevated 15 cm above the bed are 2.7 and 1.5, respectively. These trends, combined with the high coherence and small phase difference between the video and the lowest wire, demonstrate that the video-based estimates correspond to a very near-bed (less than a few centimeters elevation) wire measurement. The measured increase in runup excursion with decreasing sensor elevation and the cross-shore variation in the amplitudes of pressure fluctuations at infragravity frequencies, are consistent with the theory for linear, inviscid, normally incident standing waves. For example, valleys in the pressure spectra occur at approximately the predicted standing wave nodal frequencies. Also in accord with small-amplitude wave theory, observed swash excursions are nearly identical to pressure fluctuations at the location of the measured runup mean (for pressure sensors located seaward of the most offshore bed-level rundown). However, at very low frequencies, where reflection is typically assumed complete and dissipation negligible, the observed, near-bed swash magnitudes are overamplified relative to a best fit of the linear standing wave model based on the amplitude and phase of the seaward observations.

}, isbn = {0148-0227}, doi = {10.1029/94jc02664}, url = {In Part I, the energy levels of ocean surface waves at infragravity frequencies (nominally 0.005-0.05 Hz) locally forced by swell in 13-m water depth were shown to be predicted accurately by second-order nonlinear wave theory. However, forced infragravity waves were consistently much less energetic than free infragravity waves. Here, in Part II, observations in depths between 8 and 204 m, on Atlantic and Pacific shelves, are used to investigate the sources and variability of free infragravity wave energy. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth, but their dependencies are markedly different. Although free waves usually dominate the infragravity frequency band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water. The observed h(-1) variation of free infragravity energy with increasing water depth h is stronger than the h(-1/2) dependence predicted for leaky surface gravity waves propagating approximately perpendicular to local depth contours, but is consistent with a heuristic, geometrical optics-based (WKB) model of the refractive trapping of a directionally broad wave field generated close to shore. Preliminary analysis shows that free infragravity waves are indeed directionally broad and that the propagation directions of infragravity waves and incident swell are related. Free infragravity energy levels also depend on the general geographic surroundings. Comparisons of observations from the same depth and with similar swell conditions, but on different shelves, suggest that more free infragravity wave energy is radiated from wide, sandy beaches than from rocky, cliffed coasts and that less energy is trapped on a narrow shelf than on a wide shelf.

}, keywords = {coastal seiches, energy, generation, internal waves, model, period edge waves, surf beat}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1995)025<1063:ifhmot>2.0.co;2}, url = {The generation and propagation of infragravity waves (frequencies nominally 0.004-0.04 Hz) are investigated with data from a 24-element, coherent array of pressure sensors deployed for 9 months in 13-m depth, 2 km from shore. The high correlation between observed ratios of upcoast to downcoast energy fluxes in the infragravity (F-up(IG)/F-down(IG)) and swell (F-up(swell)/F-down(swell)) frequency bands indicates that the directional properties of up infragravity waves are strongly dependent on incident swell propagation directions. However F-up(IG)/F-down(IG) is usually much closer to 1 (i,e., comparable upcoast and downcoast fluxes) than is F-up(swell)/F-down(swell), suggesting that upcoast propagating swell drives both upcoast and downcoast propagating infragravity waves. These observations agree well with predictions of a spectral WKB model based on the long-standing hypothesis that infragravity waves, forced by nonlinear interactions of nonbreaking, shoreward propagating swell, are released as free waves in the surf zone and subsequently reflect from the beach. The radiated free infragravity waves are predicted to be directionally broad and predominantly refractively trapped on a gently sloping shelf. The observed ratios F-sea(IG)/F-shore(IG) of the seaward and shoreward infragravity energy fluxes are indeed scattered about the theoretical value 1 for trapped waves when the swell energy is moderate, but the ratios deviate significantly from 1 with both low- and high-energy swell. Directionally narrow, shoreward propagating infragravity waves, observed with low-energy swell, likely have a remote (possibly trans-oceanic) energy source. High values (up to 5) of F-sea(IG)/F-shore(IG), observed with high-energy swell, suggest that high-mode edge waves generated near the shore can be suppressed by nonlinear dissipation processes (e.g., bottom friction) on the shelf.

}, keywords = {field observations, surf beat}, isbn = {0148-0227}, doi = {10.1029/95jc02680}, url = {Infragravity waves, motions with frequencies immediately below wind-generated sea and swell, are believed to be radiated seaward from the surf zone, where they are excited by nonlinear interactions between waves in the sea-swell frequency band. We describe tidal modulation of sea surface elevation variance at infragravity frequencies observed in 8-30 m water depth, a few kilometers from shore at several California sites. Infragravity spectral levels vary by as much as a factor of 10 between high and low tide, possibly because the surf zone width and beach face slope vary significantly with tidal level on the usually concave-shaped beaches onshore of the observations. At a fixed sensor sind with approximately constant sea-swell energy, the observed infragravity energy is lowest at low tide.

}, keywords = {coastal seiches, harbor, surf beat, waves}, isbn = {0148-0227}, doi = {10.1029/95jc01545}, url = {This is Part 1 of a two-part study of infragravity-frequency (nominally 0.005-0.05 Hz) motions on the continental shelf Data from a large aperture (250 m X 250 m) array of 24 bottom-mounted pressure transducers deployed in 13 m depth is used to investigate the local forcing of infragravity motions by nonlinear difference-frequency interactions of surface gravity waves. Second-order nonlinear theory (Hasselmann) and observed swell-sea frequency-directional spectra are used to predict the energy levels of forced infragravity waves. For a wide range of wave conditions, the predicted forced wave levels are lower than the observed energy levels, suggesting that the infragravity band contains a mix of free and forced waves. Bispectral analysis is used to estimate the relative amounts of free and forced infragravity energy. Good agreement between bispectrum-based estimates and theoretical predictions of forced wave energy confirms that second-order nonlinear theory accurately predicts locally forced infragravity motions. The contribution of forced waves to the total infragravity energy, ranging from less than 0.1\% to about 30\%, is largest when the infragravity energy is maximum, consistent with previously noted trends in similar water depths. The bispectral technique developed here to estimate the energy of forced and free infragravity waves is used in Part 2 to investigate, with data from single-point pressure gauges, the shelfwide variability of free infragravity energy.

}, keywords = {generation, long waves, surf beat}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1994)024<0917:ifhmot>2.0.co;2}, url = {Linear wave theory predicts that pressure fluctuations induced by wind-generated surface gravity waves are maximum at the ocean surface and strongly attenuated at depths exceeding a horizontal wavelength. Although pressure fluctuations observed at the seafloor in deep water are indeed relatively weak at wind-wave frequencies, the energy at double wind-wave frequencies is frequently much higher than predicted by applying linear wave theory to near-surface measurements. These double-frequency waves can in theory be excited by nonlinear interactions between two surface wave components of about equal frequency, traveling in nearly opposing directions. Observations from a large aperture, 24-element array of pressure sensors deployed in 13-m depth are presented that quantitatively support this generation mechanism. As in previous studies, dramatic increases in the spectral levels of seafloor pressure at double wind-wave frequencies (0.3-0.7 Hz) frequently occurred after a sudden veering in wind direction resulted in waves propagating obliquely to preexisting seas. The observed spectral levels and vector wavenumbers of these double-frequency pressure fluctuations agree well with predictions obtained by applying second-order nonlinear, finite depth wave theory (Hasselmann, 1962) to the observed directionally bimodal seas. High-frequency seafloor pressure spectral levels also increased in response to directionally narrower but more energetic seas generated by strong, steady or slowly rotating winds. Bispectral analysis suggests that these pressure fluctuations are generated by nonlinear mechanisms similar to the veering wind cases.

}, keywords = {infrasonic ambient noise, microseisms, ocean waves, spectra, surface gravity-waves}, isbn = {0148-0227}, doi = {10.1029/94jc00054}, url = {The energy of seaward and shoreward propagating ocean surface gravity waves on a natural beach was estimated with data from an array of 24 bottom-mounted pressure sensors in 13-m water depth, 2 km from the North Carolina coast. Consistent with a parameterization of surface wave reflection from a plane sloping beach by Miche, the ratio of seaward to shoreward propagating energy in the swell-sea frequency band (0.044-0.20 Hz) decreased with increasing wave frequency and increasing wave height, and increased with increasing beach-face slope. Although most incident swell-sea energy dissipated in the surf zone, reflection was sometimes significant (up to 18\% of the incident swell-sea energy) when the beach face was steep (at high tide) and the wave field was dominated by low-energy, low-frequency swell. Frequency-directional spectra show that reflection of swell and sea was approximately specular. The ratio of seaward to shoreward propagating energy in the infragravity frequency band (0.010-0.044 Hz) varied between about 0.5 and 3 and increased with increasing swell energy. This trend suggests that infragravity waves generated in very shallow water, and refractively trapped on the sloping seabed, are significantly dissipated over a 50-km wide shelf during storms.

}, keywords = {infragravity waves, spectra}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1994)024<1503:roosgw>2.0.co;2}, url = {Turbulence generated by waves breaking on a natural beach is examined using hotfilm anemometer data. Turbulence intensity is estimated from dissipation rates determined from wavenumber spectra of short (1/8 s) hotfilm time series. The resulting Froude-scaled turbulence intensities are relatively uniform between the seabed and the wave trough level and are similar in vertical structure but lower in magnitude than in existing laboratory studies. The magnitudes of the turbulence intensities observed in both the field and laboratory are consistent with an existing macroscopic model of bore dissipation in the surf zone. Scaling by this bore model relates turbulence intensities generated by monochromatic waves in small-scale laboratory experiments to those generated by random waves in the natural surf zone.

}, keywords = {breaking waves, field, ocean}, isbn = {0148-0227}, doi = {10.1029/93jc02717}, url = {Seiche measured within a small (0.6 by 0.6 km), shallow (12-m depth) harbor is dominated by oscillations in several narrow infragravity frequency bands between approximately 10(-3) and 10(-2) Hz. Energy levels within the harbor are amplified, relative to just outside the harbor in 8.5-m depth, by as much as a factor of 20 at the lowest (grave mode) resonant frequency (approximately 10(-3) Hz) compared to amplifications of roughly 5 at higher resonant frequencies (approximately 10(-2) Hz). At nonresonant frequencies, energy levels observed inside the harbor are lower than those outside. These amplifications are compared to predictions of a numerical model of seiche excited by linear, inviscid long waves impinging on a harbor of variable depth. The amplification of higher-frequency (approximately 10(-2)-Hz) seiches is predicted within a factor of about 2. However, at the grave mode (10(-3) Hz), the observed amplification decreases with increasing swell and seiche energy levels, possibly owing to the sensitivity of this highly amplified mode to dissipation not included in the inviscid model. The energy levels of higher-frequency seiche within the harbor were predicted from the offshore sea and swell spectra by the ad hoc coupling of the linear model for the amplification of harbor modes with a nonlinear model for the generation of bound infragravity waves outside the harbor. The predictions are qualitatively accurate only when the swell is energetic and bound waves are a significant fraction of the infragravity energy outside the harbor.

}, keywords = {coastal seiches, infragravity waves, internal waves, oscillations, sea}, isbn = {0148-0227}, doi = {10.1029/93jc01760}, url = {Shoaling wave fields generated in laboratory experiments were analyzed to determine the sensitivity of nonlinear interactions to the directional distributions of incident waves. Peaks in the directional spectra observed in shallow water were consistent with near-resonant, quadratic interactions between two primary waves transferring energy to a third wave with the sum frequency and vector sum wavenumber of the primary waves. Directionally colinear waves forced a higher-frequency wave propagating in the same direction as the primary waves, while directionally spread (i.e., noncolinear) primary waves forced a higher-frequency wave that propagated in a direction between those of the interacting primary waves. Deepwater wave fields with similar frequency spectra but different directional spectra evolved to different shallow-water directional spectra, yet their shallow-water frequency spectra were remarkably similar. This result suggests that the shape of the directional spectrum of the incident wave field has only a small effect on the magnitudes of nonlinear energy transfers during shoaling. The principal effect of directionality in the incident wave field is on the directions, not the amplitudes, of the nonlinearly generated waves. The laboratory data demonstrate clearly the importance of triad interactions between noncolinear and colinear shoaling waves.

}, keywords = {diffraction, model, refraction, shallow-water, spectra, transformation}, isbn = {0148-0227}, doi = {10.1029/93jc02213}, url = {Two models, a spectral refraction model (Longuet-Higgins) and a parabolic equation method (PEM) refraction-diffraction model (Kirby), are used to simulate the propagation of surface gravity waves across the Southern California Bight. The Bight contains numerous offshore islands and shoals and is significantly larger (almost-equal-to 300 km by 300 km) than regions typically studied with these models. The effects of complex bathymetry on the transformation of incident wave directional spectra, S0(f,theta0), which are very narrow in both frequency and direction are difficult to model accurately. As S0 (f, theta0) becomes broader in both dimensions, agreement between the models improves and the spectra predicted at coastal sites become less sensitive to errors in the bathymetry grid, to tidal changes in the mean water depth, and to uncertainty in S0(f,theta0) itself. The smoothing associated with even relatively narrow (0.01 Hz-5-degrees bandwidth) S0 (f,theta0) is usually sufficient to bring the model predictions of shallow water energy into at least qualitative agreement. However, neither model is accurate at highly sheltered sites. The importance of diffraction degrades the predictions of the refraction model, and a positive bias [O(10\%) of the deep ocean energy] in the refraction-diffraction model estimates, believed to stem from numerical {\textquoteright}{\textquoteright}noise{\textquoteright}{\textquoteright} (Kirby), may be comparable to the low wave energy. The best agreement between the predicted spectra generally occurs at moderately exposed locations in deeper waters within the Bight, away from shallow water diffractive effects and in the far-field of the islands. In these cases, the differences between the models are small, comparable to the errors caused by tidal fluctuations in water depth as waves propagate across the Bight. The accuracy of predicted energies at these sites is likely to be limited by the uncertainty in specifying S0(f,theta0).

}, keywords = {diffraction, directional spectra, parabolic equation method}, isbn = {0378-3839}, doi = {10.1016/0378-3839(93)90032-4}, url = {Statistics of wave groups observed for a wide range of wave heights, power-spectral shapes, and water depths are compared to the statistics predicted by both direct numerical simulation and analytic approximation of linear wave theory. Comparisons to numerical simulations show that the observed groups are not inconsistent with linear, Gaussian wave fields with the same spectra as the observations. Differences between ocean observations and linear theory are owing to statistical fluctuations in group statistics estimated with the 2.3-h-long data records. One linear analytic model accounts for correlations between two successive waves, and slightly underpredicts the average number of sequential large waves for wave fields with very narrow power spectra. A newly developed extension to Rice better accounts for multiwave correlations, but has only marginally improved accuracy for these data because wave fields with very narrow power spectra rarely occurred. Both approximations overpredict the group lengths for very broad and/or multipeaked power spectra, but are still useful because the errors are small with commonly occurring spectral shapes. Direct numerical simulations, with computational expense between that of the spectral-Kimura and extended-Rice approximations, yield the best predictions of the observed wave group statistics given a power spectrum, and also provide estimates of the statistical fluctuations of group properties about predicted mean values.

}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1993)119:2(144)}, url = {The roles of frequency dispersion, nonlinearity, and laminar viscosity in the evolution of long waves over distances of many wavelengths in constant water depth are investigated with numerical solutions of the Boussinesq equations. Pronounced frequency doubling and trebling is predicted, and the initial evolution to a wave shape with a pitched-forward front face and peaky crests is followed by development of a steep rear face and a nearly symmetric crest/trough profile. While reducing overall energy levels, laminar viscosity acts to prolong cycling of third moments and to inhibit the onset of disordered evolution characteristic of nonlinear, inviscid systems. Preliminary laboratory results show some qualitative similarities to the numerical simulations. However, these laboratory experiments were not suitable for detailed model-data comparisons because dissipation in the flume could not be accounted for with either laminar or quadratic damping models. More carefully controlled experiments are required to assess the importance of viscosity (and the accuracy of the Boussinesq model) in the evolution of nonlinear waves over distances of many wavelengths.

}, keywords = {bispectra, model, surface gravity-waves}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1993)119:4(351)}, url = {Infragravity-wave (periods of one-half to a few minutes) energy levels observed for about 1 year in 8-water depth in the Pacific and in 8- and 13-m depths in the Atlantic are highly correlated with energy in the swell-frequency band (7- to 20-s periods), suggesting the infragravity waves were generated locally by the swell. The amplification of infragravity-wave energy between 13- and 8-m depth (separated by 1 km in the cross shore) is about 2, indicating that the observed infragravity motions am dominated by free waves, not by group-forced bound waves, which in theory are amplified by an order of magnitude in energy between the two locations. However, bound waves am more important for the relatively few cam with very energetic swell, when the observed amplification between 13- and 8-m depth of infragravity-wave energy was sometimes 3 times greater than expected for free waves. Bispectra are consistent with increased coupling between infragravity waves and groups of swell and sea for high-energy incident waves.

}, keywords = {edge waves, long waves}, isbn = {0148-0227}, doi = {10.1029/92jc01316}, url = {This is Part 2 of a study of nonlinear effects on natural wind-generated surface gravity waves in 13-m depth, 30 km offshore of Virginia. At the sea floor in this depth, free surface gravity waves are only weakly attenuated at sea and swell frequencies (0.05-0.30 Hz) but are very strongly attenuated at frequencies higher than about 0.35 Hz. Hence, above 0.35 Hz, relatively long wavelength forced waves, excited by nonlinear interactions between directionally opposing free wind waves, are exposed at the sea floor. An array of pressure transducers at middepth was used to estimate the frequency-directional spectrum of (free) primary sea and swell waves, and the associated (forced) secondary pressure fluctuations were measured with an array on the sea floor. In Part 1, it was shown that forced-wave energy levels at the sea floor increase sharply in response to directionally opposing wind waves, in agreement with weakly nonlinear theory. In Part 2, wavelengths, propagation directions, and non-Gaussian phase coupling between free and forced waves are examined on three occasions with relatively high forced-wave energy levels. A root-mean-square wavenumber magnitude and a vector-averaged mean wave propagation direction (both functions of frequency) can be expressed accurately in terms of the pressure array cross-spectra. The wavenumber estimates at the sea floor show the theoretically expected sharp transition between a 0.05-0.30 Hz frequency range dominated by free sea and swell waves and a 0.35-0.60 Hz range dominated by forced waves with wavelengths that are long relative to free waves of the same frequency. In the "free-wave frequency range," wavenumber estimates are usually well within 10\% of the linear dispersion relation and wave direction estimates are in excellent agreement with the directional spectra extracted from the middepth an-ay. In the "forced-wave frequency range," wavenumber and direction estimates agree with nonlinear theory predictions, confirming that the observed forced waves have the sum vector wavenumber of the interacting directionally opposing wind waves. Phase coupling between free and forced waves is examined through third-order statistics of the sea floor pressure data. Consistent with theory, the normalized bispectrum has small imaginary parts scattered approximately randomly about zero and relatively large negative real parts at frequencies that correspond to directionally opposing seas and swell. Estimates of the bispectrum integrated for constant sum frequency confirm that nearly all the energy at double sea frequencies is nonlinearly coupled to directionally opposing wind waves. In qualitative agreement with nonlinear theory predictions, bispectral levels are sometimes significantly reduced by directional spreading of the interacting free waves.

}, keywords = {array, directional spectra, ocean, random gravity-waves, seafloor microseisms, water}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1992)022<0489:wwnoat>2.0.co;2}, url = {Model predictions of bound (i.e. nonlinearly forced by and coupled to wave groups) infragravity wave energy are compared with about 2 years of observations in 8- to 13-m depths at Imperial Beach. California, and Barbers Point. Hawaii. Frequency-directional spectra of free waves at sea and swell frequencies, estimated with a small array of four pressure sensors, are used to predict the bound wave spectra below 0.04 Hz. The predicted total bound wave energy is always less than the observed infragravity energy, and the underprediction increases with increasing water depth and especially with decreasing swell energy. At most half, and usually much less, of the observed infragravity energy is bound. Bound wave spectra am also predicted with data from a single wave gage in 183-m depth at Point Conception, California, and the assumption of unidirectional sea and swell. Even with energetic swell, less than 10\% of the total observed infragravity energy in 183-m depth is bound. Free waves, either leaky or edge waves, are more energetic than bound waves at both the shallow and deep sites. The low level of infragravity energy observed in 183-m depth compared with 8- to 13-m depths, with similarly moderate sea and swell energy, suggests that leaky (and very high-mode edge) waves contribute less than 10\% of the infragravity energy in 8-13 m. Most of the free infragravity energy in shallow water is refractively trapped and does not reach deep water.

}, keywords = {array, dependency, edge waves, generation, inshore long waves, offshore short waves, surf beat}, isbn = {0148-0227}, doi = {10.1029/92jc00270}, url = {Field observations of a shoaling, nonbreaking, directionally spread wave field are simulated in a laboratory basin to determine whether laboratory artifacts cause significant distortions of the shoaling process. The laboratory wave field is measured with scaled arrays of surface-elevation sensors similar to the arrays used for the field observations. However, differences in the laboratory and field beach slopes (0.033 and 0.025, respectively) do not allow precise replication of the field conditions in the laboratory. Therefore, a nonlinear wave propagation model with no adjustable parameters (previously successfully compared to a wide range of field data) is used to show that differences between the laboratory and field data sets are caused primarily by the different beach slopes. The observations demonstrate, in agreement with the model, that it is possible to compensate partially for differences in beach slope by altering the initial conditions. With such compensation, the evolution of surface-elevation power spectra, bispectra, and skewness and asymmetry are remarkably similar in the laboratory and field. Frequency-directional spectra measured just outside the surf zone also show similar nonlinear effects in both field and laboratory data. Based on this case study, the laboratory directional wave basin appears to be useful for investigating the linear and nonlinear evolution of random, two-dimensional waves on beaches.

}, keywords = {beach, bispectra, model, nonlinear refraction diffraction, shallow-water, surface gravity-waves}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1992)118:1(87)}, url = {Field measurements of wave orbital velocities and pressure, collected in the lower part of the water column in 7 m depth with a three-component acoustic Doppler current meter and a co-located pressure transducer, are compared to the second-order theory for weakly nonlinear surface gravity waves in arbitrary water depth (Hasselmann 1962). Pressure and velocity spectra and cross-spectra are in excellent agreement with (linear) free wave transfer functions, even at (and higher than) twice the spectral peak frequency where nonlinearities (forced secondary waves) are expected to be important. Theoretical predictions show that although secondary waves sometimes contribute a significant fraction of the energy observed at double swell and sea frequencies, their effect on velocity-pressure transfer functions is small. However, forced waves are more apparent in deviations from Gaussian statistics. Good agreement between observed and predicted third-order statistics shows that Hasselmann{\textquoteright}s weakly nonlinear theory accurately describes the secondary pressure and orbital velocity (both horizontal and vertical components) field at double swell and sea frequencies, even for moderately large (O(0.1-0.2)) values of the nonlinear perturbation parameter. Only with near-breaking swell and relatively strong nonlinearities (perturbation parameter almost-equal-to 0.22), do the observed third-order statistics diverge significantly from Hasselmann{\textquoteright}s theory.

}, keywords = {depth, directional spectra, moments, verification, water}, isbn = {0022-1120}, doi = {10.1017/s0022112092000521}, url = {A model for the propagation of sea and swell waves in a channel bounded by rubble-mound jetties is presented. The model combines elements of earlier work on waves normally incident on a breakwater with a modified diffraction model based on the linear mild-slope equation. For grazing-angle (relative to the jetty axis) wave incidence, a parabolic approximation to the governing equation is used to obtain numerical solutions for monochromatic long waves propagating down the channel. An initially plane wave evolves into a spatially complex pattern as dissipation occurs along the jetties and energy is drawn from the channel interior by diffraction. Comparisons of the model to field observations are presented in a companion paper.

}, keywords = {diffraction, energy-dissipation, friction, reflection, water-waves}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1991)117:5(471)}, url = {Field measurements of surface gravity waves along the center line of the straight, 1 km long, 8 m deep, 250 m wide Mission Bay entrance channel (bounded by rubble-mound jetties) are compared to a model developed in a companion paper by Melo and Guza. The observations show a rapid downchannel decay of wave energy. Additionally, the observed ratio of significant wave heights between any two stations along the channel axis is rather constant despite the different wave and current conditions encountered. The model, with all empirical coefficients determined with existing parameterizations, agrees qualitatively well with these observations. These model results are insensitive to the details of the motions and dissipation occurring within the jetties so long as an appropriate amount of energy is lost at these lateral boundaries. The wave height on the center line of a wide channel with highly absorptive jetties is controlled by diffraction. In fact, the observations and model results on the center line at Mission Bay are similar to previously published simplified models with the jetties replaced by strips of appropriate bottom dissipation and also to the decay along the center line of a breakwater gap with the gap width equal to the entrance channel width.

}, keywords = {bottom, energy-dissipation, reflection}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1991)117:5(493)}, url = {A compact acoustic Doppler current meter, designed for nearshore surface gravity wave measurements, was field tested by comparison to a colocated array of pressure transducers. Both measurement systems were bottom mounted in a water depth of 7 m. Each of four acoustic beams, inclined 45-degrees from vertical, measures the along-beam velocity at a single range (1 m) about 1.5 m above the seafloor. These four velocity beams are used to estimate low-order moments of the frequency-directional wave spectrum and are compared to pressure measurements on four occasions. Predictions of the (nondirectional) bottom pressure spectrum at sea and swell frequencies (0.04-0.30 Hz), based on the velocity measurements and linear theory, are in excellent agreement with directly measured pressure. The general level of agreement (gain errors less than 5\%) is somewhat better than results reported from similar (but spanning a much wider range of conditions) intercomparison studies using conventional in situ current meters. Observed cross spectra between colocated pressure and horizontal velocity components, frequently used to separate turbulence and wave orbital velocities (assuming that the coherence of wave velocity and pressure is equal to 1), are compared to predictions based on the pressure array data and linear wave theory. The observed and predicted pressure-velocity cross spectra are in excellent agreement and show that large coherence reductions can occur in natural wind waves owing to wave directional spreading effects, despite relatively low turbulence energy levels. Wave radiation stresses, estimated from the velocity measurements, also agree well with estimates extracted from the pressure array data. Overall, the intercomparisons show that the present acoustic Doppler system has directional resolution comparable to a pitch-and-roll buoy, and they suggest that higher-order directional information as well as weak nonlinear properties of natural wind waves may be examined with a slightly modified compact system.

}, keywords = {layer, ocean, spectra, velocities}, isbn = {0148-0227}, doi = {10.1029/91jc01326}, url = {Wave energy estimated from linear, spectral wave propagation models incorporating refraction and refraction-diffraction are compared over two bottom configurations: an analytic circular shoal and relatively smooth coastal bathymetry from San Diego, California. The agreement between the two models improves with an increase in the width of the incident directional spectrum and with a decrease in the complexity of the local bathymetry. There are, however, significant differences between the model transformations of directionally narrow spectra on both bathymetries. Pure refraction models are not quantitatively accurate in these cases. These comparisons also demonstrate the importance of directional wave spreading in transformations over even relatively simple natural bathymetry. Data from a fundamentally low-resolution pitch-and-roll buoy, if used as the sole source of directional information for incident waves, can lead to significant uncertainty in wave heights estimated by the refraction-diffraction model.

}, keywords = {angle water-waves, approximations, parabolic equation method, propagation}, isbn = {0733-950X}, doi = {10.1061/(asce)0733-950x(1991)117:3(199)}, url = {This is Part 1 of a study of nonlinear effects on natural wind waves. Array measurements of pressure at the sea floor and middepth, collected 30 km offshore of Virginia in 13-m depth, are compared to an existing theory for weakly nonlinear surface gravity waves. In this depth, free surface waves (obeying the linear dispersion relation) are weakly attenuated at the sea bed at sea and swell frequencies (0.05-0.3 Hz) but very strongly attenuated at frequencies higher than about 0.35 Hz. Only nonlinearly driven motions can reach the sea floor at these high frequencies. Nonlinear interactions between free (primary) waves of about the same frequency, traveling in nearly opposing directions, theoretically excite long-wavelength, double-frequency forced (secondary) waves that are only weakly attenuated at the sea floor and form a mechanisms for the generation of microseisms at great depth. In 13-m depth, wind-generated free waves and corresponding long-wavelength, high-frequency forced waves can be simultaneously observed on the sea floor, and the coupling between the two examined in some detail. Bottom-pressure spectra observed over a 4-day period show large [O(10(2))] fluctuations in high-frequency (0.35-0.6 Hz) forced-wave energy levels at the sea floor occurring in only a few hours. Correspondingly rapid changes in estimates of the free-wave frequency-directional spectrum show that forced-wave energy levels are weak in unidirectional seas and increase dramatically in response to nearly opposing seas, consistent with the theoretical generation mechanism. On one occasion, directionally opposing seas, and a corresponding double-frequency forced-wave peak, followed a rapidly veering wind. However, comparable increases in forced-wave energy levels were observed in response to the arrival of nonlocally generated seas with directions much different than local winds and seas. Although the accuracy of theoretical forced-wave predictions is limited by the directional resolution of the small aperture (20 m x 20 m) middepth array, predicted and observed forced-wave energy levels agree within about a factor of 2. The observed weak decay between middepth and sea-floor wave pressure at double sea frequencies is also consistent with theoretically expected long wavelengths. Wavelengths, propagation directions, and phase coupling between free and forced waves are examined using the bottom-pressure array data in Part 2.

}, keywords = {directional spectra, ocean, random gravity-waves, seafloor microseisms, water}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1991)021<1740:wwnoat>2.0.co;2}, url = {The predictions of linear and nonlinear (Boussinesq) shoaling wave models for nonbreaking unidirectional surface gravity waves are compared to field observations, with particular emphasis on quantities that may be important for cross-shore sediment transport. The extensive data sets were obtained on two natural beaches, span water depths between 1 and 10 m, and include incident wave power spectra with narrow, broad, and bimodal shapes. Significant wave heights varied between approximately 30 and 100 cm, and peak periods between approximately 8 and 18 s. The evolution of total variances of sea surface elevation, cross-shore velocity, and horizontal acceleration is modeled at least qualitatively well by both linear and nonlinear theories. Only the nonlinear theory predicts the increasingly asymmetric sea surface elevations and horizontal velocities (pitched-forward wave shapes) and the weaker variation of skewness (difference between crest and trough profiles) which are observed to occur during shoaling. The nonlinear theory also models qualitatively well the large skewed accelerations which occur during the passage of asymmetric waves.

}, isbn = {0148-0227}, doi = {10.1029/JC095iC09p16055}, url = {A limitation on the performance of complex empirical orthogonal function (CEOF) analyses in the time domain is illustrated with synthetic, noise-free, nondispersive, propagating signals. Numerical examples using a band-limited white spectrum and a simulation of costal-trapped waves sampled with an array of tide gauges, demonstrate that CEOF analysis is degraded with increasing ΔκΔχ (Δκ is the wavenumber bandwidth and Δχ is the instrument array length). A relatively wide wavenumber bandwidth [ΔκΔχ \< 0(2π)] results in a significant loss of variance recovery towards the ends of the array. The CEOF method don yield an average frequency and wavenumber for the first mode, independent of ΔκΔχ, that accurately estimate the phase speed of the nondispersive propagating signal. These simple simulators indicate that modal spatial patterns from a time domain CEOF analysis of wide-banded signals should be interpreted cautiously.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1990)020<1628:dpswce>2.0.co;2}, url = {An improved method for estimating the directional spectrum of linear surface gravity waves from in Situ observations is presented. The technique, a refinement and extension of the inverse method of Long and Hasselmann, is applicable to multicomponent wave measurements at fixed locations in constant or slowly varying depth water. On a frequency band by frequency band basis, an estimate of the directional distribution of wave energy S(θ) is obtained by minimizing a roughness measure of the form ∫dθ[d2S(θ)/dθ2]2 subject to the constraints: (i) S(θ) is nonnegative with unit integral, (ii) S(θ) fits the data within a chosen statistical confidence level, and (iii) S(θ) is zero on any directional sectors where energy levels are always relatively low because of the influence of geographic surroundings. The solution to this inverse problem is derived through a variational formulation with Lagrange multipliers.A series of simulations using the new estimator show the fundamental limitations of sparse array data and the importance of using all available data-independent information [i.e., constraints (i) and (iii)] for achieving optimal estimates. The advantages of smoothness optimization are illustrated in a comparison of the present and Long and Hasselmann methods. The present method yields smooth estimates where Long and Hasselmann obtained rough estimates with multiple spurious peaks. A smooth solution to the inverse problem that has only truly resolved features is both easier to interpret and more readily evaluated numerically than wildly spurious solutions. The examples also demonstrate the subjectivity of intercomparing estimation techniques.A few illustrative examples are presented of S(θ) estimates obtained from a two-dimensional array (aperture 120 m {\texttimes} 96 m) of 14 pressure transducer in 6 m water depth. Estimates using the full array and no geographic constraints are smooth and exhibit the expected refractive columnation of shoreward propagating energy towards normal incidence. Additionally, reflection from the mildly sloping beach 310 m shoreward of the center of this array is very weak at wind wave and swell frequencies. Estimates of S(θ) made using only the sensors on a longshore line, and a constraint of no reflected energy, are very similar to S(θ) obtained with the full array and no constraint.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1990)020<1703:eodwsf>2.0.co;2}, url = {The spatial evolution of a directionally spread wave field on a near-planar natural beach is examined using data from longshore arrays of pressure sensors and wave staffs at 10.3 m and 4.1 m depth. High-resolution frequency-directional spectra from the deeper array are used to initialize a linear refraction model, and the resulting model predictions are compared with frequency-directional measurements at the shallow array. Linear theory inaccurately predicts both the shapes of directional spectra in shallow water and the total variances in some frequency bands. The discrepancies are largest for frequencies associated with maxima in the bicoherence spectrum, suggesting the importance of nonlinear effects. Furthermore, the measured directional spectrum at energetic low frequencies (0.05{\textendash}0.11 Hz) and the vector resonance conditions for triads of long waves can be used to predict accurately the directions of observed peaks in directional spectra at higher frequencies (0.12{\textendash}0.21 Hz). Prominent features in the measured directional spectra at the shallow array are thus consistent with energy transfers resulting from near-resonant triad interactions in the shoaling wave field.

}, isbn = {0148-0227}, doi = {10.1029/JC095iC06p09645}, url = {The rapid spatial recurrence of weakly nonlinear, weakly dispersive, progressive shallow-water waves is examined with numerical simulations using a discretized and truncated (i.e., finite number of allowed frequency modes) form of the Boussinesq equations. Laboratory observations of sandbar formation under recurring, mechanically generated monochromatic waves with small Ursell number have motivated others to suggest that recurrence in naturally occurring random waves contributes to the establishment of periodic longshore sandbars on beaches. The present study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that rapid spatial recurrence is not an inherent property of discretized and truncated Boussinesq systems for evolution distances of 10{\textendash}50 wavelengths. When a small number of Fourier modes are used to represent an initially monochromatic wave field with significant nonlinearity (the Ursell number is O(1)), there is a trend toward recurrence of initial modal amplitudes, consistent with the known periodic solutions for a primary wave and its harmonic. However, for 32 modes or more, numerical simulations indicate only a few cycles of a damped recurrence, followed by disordered evolution of the Fourier amplitudes. For initial conditions similar to ocean field measurements of frequency-sorted swell with Ursell number O(1) and many (\>300) modes in the numerical model, the Fourier coefficients of the wave field do not recur rapidly. Thus in these cases the predictions of many rapid recurrence cycles by few-mode models is an artifact of severe truncation. On the other hand, even with many allowed modes, pronounced recurrence is predicted when the Ursell number is small and the initial wave field is monochromatic. In this case, few- and many-mode solutions are similar.

}, isbn = {0148-0227}, doi = {10.1029/JC095iC07p11547}, url = {A compact array of four bottom-mounted pressure sensors arranged in a square, a slope array, is frequently used to obtain estimates of the wave radiation stresses in shallow water. For wavelengths long in comparison with the array dimension (L), existing processing methods (Higgins et al., 1981) have bias errors of O(kL)2, with k the wavenumber. An estimator for wave radiation stresses and energy fluxes is derived here that reduces the bias to O(kL)4, thus considerably extending the frequency range of accurate estimates of a slope array. The stability of the new estimator to statistical fluctuations in the cross spectra is similar to the method of Higgins et al. [1981].

}, doi = {10.1029/JC094iC02p02099}, url = {Numerical simulations are used to investigate statistics of biocoherence for the special case of a linear random process. Smoothed bicoherence statistics are shown to be independent of both the normalization used to form the bicoherence and of whether statistical stability is obtained by ensemble-averaging short records, or frequency merging within a long record

}, isbn = {0096-3518}, doi = {10.1109/29.7555}, url = {Laboratory and field measurements of suspended sediment in the nearshore suggest that fluid accelerations are an important factor in sediment transport by oscillatory waves. Here, Eulerian accelerations of the cross-shore velocity are calculated from measurements of velocity obtained by an array of bottom-mounted electromagnetic flow meters spanning a natural surf zone. Large shoreward accelerations of brief duration are associated with the steep front faces of both near-breaking and breaking waves. Weaker offshore accelerations of longer duration occur during passage of the more gently sloped rear faces. The acceleration field is thus strongly skewed in the shoreward direction. Power spectra and bispectra indicate, as expected, that statistics of the acceleration field are significantly influenced by high-frequency motions but are rather insensitive to surf beat.

}, doi = {10.1029/JC093iC08p09261}, url = {In order to assess the performance of current meters within and near the surf zone, data from biaxial electromagnetic current meters with spherical and open frame probe geometries were intercompared. One bottom-mounted flow meter of each type was deployed in a mean depth of 7.0 m for 17 days, and two sensors of each type were deployed in a mean depth of 2.0 m for 5 days. Sensors in the shallow deployment were frequently in the surf zone. Hourly averaged mean flows measured by different sensor types are highly correlated, averaging above 0.98. The largest difference between measured mean flows is a constant bias, typically about 3.0 cm/s, which is roughly equal to the estimated accuracy of the sensor offset calibrations. Root-mean-square deviations from this constant bias are less than 2.0 cm/s, and are contributed to by errors in both gain calibration and sensor orientation. Comparisons of measured (surface gravity wave) oscillatory currents were made both between current meter types and with velocities inferred from the application of linear theory to pressure sensor data. Correlations between time series of UTrms (the rms total oscillatory velocity for a 1-hour record) were all above 0.99 in 7.0-m depth and averaged 0.95 for the shallow deployment. The average UTrms ratio (over all hour-long records) was within 1.0 {\textpm}0.07 for all current meter pairs in both deployments, which is consistent with the estimated 5\% uncertainties in the flow meter gain calibration. Typical fluctuations of the UTrms ratio of any spherical and open frame sensor pair about its mean ratio, indicative of flow meter gain distortions probably associated with variations in the hydrodynamic environment, were less than 0.04 for any one deployment. Ratios of UTrms from both deployments taken together suggest that the open frame sensor overresponds, relative to the spherical probe, by about 5\% at low (about 10.0 cm/s) total (mean + UTrms) speeds, and underresponds by about 5\% at higher total speeds of about 75 cm/s. Relative to pressure data and linear theory, both flow meter types overrespond at low total speeds and underrespond at high total speeds. We are, however, unable to determine whether these apparent gain deviations (of less than 10\%) of the flow meters relative to pressure are associated with errors in the linear theory used to convert pressure to velocity, or with the response characteristics of the flow meters. Cross spectra between all sensors (including pressure) show high coherence and phase differences of a few degrees, and they suggest that the response of both flow meters is only slightly frequency dependent. Various practical difficulties in accurately measuring the flow-induced microvolt potentials in electromagnetically noisy environments, with potentially interfering current meters, are discussed.

}, doi = {10.1029/JC093iC08p09302}, url = {Wavenumber-frequency spectra of the infragravity (periods 20-200 sec) wave velocity field in the surf zone of two California beaches are estimated. Because the longshore arrays of biaxial electromagnetic current meters are relatively short (comparable to the wavelengths of interest), high resolution spectrum estimators are required. Model testing provides insight into the limits, capabilities and reliability of the estimators used in this paper. On all 15 days analyzed, between 42\% and 88\% of the longshore current variance at the array is contributed by low mode (n<=2) edge waves. (Percentage estimates are not made at a few frequencies because the array is positioned near nodes.) The low mode signal in the cross-shore velocity at the arrays is usually masked by unresolvable high mode and/or leaky waves. The percentage of cross-shore current variance at the array estimated unresolvable high mode is less than 35\%, with one exception for which approximately 50\% of the variance is mode 0 across a substantial portion of the infragravity band. On average, low mode (n<=2) edge waves constitute 69\% (17\%) of the variance of the longshore (cross-shore) infragravity velocities at both arrays. There are days at both beaches that show factors of 3 asymmetry in the energy of up and downcoast progressive edge waves of a particular mode number, but the ratio of up and downcoast energy of up and downcoast progressive edge waves of a particular mode number, but the ratio of up and downcoast energy is usually within 1{\textpm}0.1 On 8 of the 15 days, the spectrum of swash motions on the beach face is measured with a run-up meter. The swash spectrum, an estimate of the one-dimensional (summed over all wavenumbers) infragravity shoreline elevation spectrum, is compared to the edge wave shoreline elevation variances inferred from the velocity measurements at the array. As much as 50\% of the variance in the present dataset, low mode edge waves contribute significantly to both the longshore velocity and run-up components of the nearshore infragravity wave field. Daily fluctuations in the shoreline elevation variance of individual low mode edge waves are regressed against the total wind and swell wave variance (periods 3{\textendash}20 sec) measured outside the surf zone. The correlations are statistically significant at one beach, but not the other. Distortions of the observed edge wave dispersion curved (from a plane beach solution) because of beach concavity and mean longshore currents are small but detectable.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1987)017<0644:iewoot>2.0.co;2}, url = {Steady surf-zone longshore currents and directional properties of the incident wave field were measured on a beach with nearly straight and parallel depth contours. Selected data were processed into 64 segments, each of 68.2 min. duration, irregularly spaced throughout an 18-day period. A wide variety of incident wave and longshore current conditions were observed. The radiation stress spectrum [Sxy(f)] was estimated from a slope array and two current meters located seaward of the surf zone. In many cases the total radiation stress [SxyT = ΣSxy(f)Δf] contains important contributions from a wide range of frequencies. In a few instances, sea and swell approach the beach from different directions quadrants resulting in a new zero SxyT. The strong shears and direction reversals of the longshore current that could conceivably occur in this circumstance were not observed. An EOF decomposition of the mean longshore current pattern shows that most (\<90\%) of the current spatial variation in the 64 runs is contained in a classical parabolic shape. The temporal expansion coefficients of the first EOF are equally highly correlated with both SxyT, and a scale velocity suggested by radiation stress-based longshore current theories.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1986)016<1959:ooslci>2.0.co;2}, url = {Boussinesq-type nonlinear equations for waves propagating over a sloping bottom are shown to accurately model the evolving bispectra of a spectrum of non-breaking shoaling ocean-surface gravity waves. The model response to a variation of the gentle, constant beach slope and the amount of nonlinear (i.e. non-random) phase coupling in the initial conditions is also examined. Variation of these quantities results in relatively little change in the overall structural evolution of the bicoherence and biphase (related to the nonlinear modification of the wave shape). The apparent unimportance of bottom slope motivates consideration of constant-depth KdV equations. Simple analytic solutions are found for harmonic growth in the special case of a monochromatic primary wavetrain. The associated bispectral evolution is qualitatively similar to field observations and to predictions based on the full Boussinesq model for a sloping bottom.

}, isbn = {0022-1120}, doi = {10.1017/s0022112086002690}, url = {Analytic and numerical models for longshore currents generated by obliquely incident random waves am compared with field observations. Five days of observations were selected during which the waves were narrow banded in both frequency and direction, in keeping with model assumptions. The extensive measurements included radiation stress and wave directional spectra in 9 m depth, and a closely spaced array of current and pressure sensors on a line perpendicular to shore. The longshore current models are based on balancing the gradient of the radiation stress with the alongshore bed shear and Reynold{\textquoteright}s stresses, assuming stationary wave conditions and straight and parallel bottom contours. The spatial variation of wave height, required to determine the gradient of the radiation stress, is modeled using linear random wave theory. Given Hrms in 9 m depth, the model predicts Hrms at shoreward locations with an average error of less than 9\%. Using a nonlinear bottom shear stress formulation and the measured topography, a bed shear stress coefficient of cf = 0.006 gives optimal agreement between observed and predicted longshore currents. Eddy viscosity was found not to be important, at least for the nearly planar topography present during the observations.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1986)016<1165:szlcar>2.0.co;2}, url = {Aspects of the nonlinear dynamics of waves shoaling between 9 and 1 m water depths are elucidated via the bispectrum. Bispectral-signal levels are generally high, indicating significant nonlinear coupling. In 9 m depth, the biphases of interactions involving frequencies at, and higher than, the peak of the energy spectra are suggestive of Stokes-like nonlinearities (Hasselman, Munk \& MacDonald 1963). Further shoaling gradually modifies these biphases to values consistent with a wave profile that is pitched shoreward, relative to a vertical axis. Bicoherence and biphase observations with a double-peaked (swell and wind-wave) power spectrum provide evidence for excitation of modes at intermediate frequencies via difference interactions, as well as the sum interactions responsible for harmonic growth. Shoreward-propagating low-frequency (surf-beat) energy is shown to have statistically significant coupling to higher-frequency modes within the power-spectral peak. In 18 m depth, the biphase of these interactions is close to 180{\textdegree}, a value consistent with the classical concept of bound long waves. In shallower water, however, substantial biphase evolution occurs, and there is no longer a unique phase relationship between surf beat and the envelope of high-frequency waves. The contributions to sea-surface-elevation skewness and asymmetry (with respect to a vertical axis) from interactions among various wave triads are given by the real and imaginary parts of the bispectrum, respectively. In very shallow water, coupling between surf beat and higher-frequency waves results in a skewness with sign opposite to, and about 40\% of the magnitude of, the skewness resulting from interactions between the power-spectral-peak frequency and higher frequencies.

}, isbn = {0022-1120}, doi = {10.1017/s0022112085003007}, url = {The magnitudes of cross-shore velocity and elevation oscillations at surf beat frequencies observed on three ocean beaches are significantly correlated with the significant height of incident wind waves. Measured surf beat run-up spectra are coupled with numerical integrations of the long wave equations to predict the energy spectrum at offshore sensors, and the coherence and phase between offshore sensors and run-up meter. As in previous studies, valleys in the observed surf beat energy spectra at offshore sensors, and jumps in the relative phase between sensors, occur at the nodal frequencies of simple standing wave (either leaky or high mode edge wave) models. The variance observed in the surf beat cross-shore velocity field is between 10 and 100 times larger near the shoreline than in 5 m depth, and decays more rapidly with increasing offshore distance than the variance in the surf beat elevation field. The standing wave model is qualitatively consistent with this structure.

}, doi = {10.1029/JC090iC02p03161}, url = {Observed statistics of non-breaking ocean-surface gravity waves shoaling between 4 and 1 m depths are compared with the predictions of linear finite-depth theory and a nonlinear model. The linear theory included effects of the directional distribution of energy within each frequency component. The nonlinear model, which does not consider directional effects, is based on Boussinesq-type equations for a sloping bottom (Freilich \& Guza 1984). Given initial conditions in 4 m depth, the nonlinear model more accurately predicts the evolution of energy spectra, coherence and phase speed between sensors, and lengths of runs of high waves than does the linear theory. In four out of five cases, observed trends in the evolution of sea-surface-elevation skewness are predicted by the nonlinear model, while linear theory predicts zero skewness. Neither model can explain changes in the directional spectra observed between 9 and 4 m depths.

}, isbn = {0022-1120}, doi = {10.1017/s0022112085002543}, url = {Recent models for nearshore sediment transport suggest the importance of various moments of the fluid velocity field in determining transport rates. Using two days of field data from a low slope beach with moderate wave heights (H\~{}70cm), some low order, normalized moments are compared to results from simple monochromatic and linear random wave models. Not surprisingly, the random wave model is substantially more accurate than the monochromatic model. However, wave breaking and other nonlinearities introduce effects not explained by either formalism. The observed cross-shore velocity variance is decomposed into wind wave and surf beat components. The surf beat contribution is maximum at the shoreline, while the wind wave component is maximum offshore. The total variance is nearly constant across the surf zone. This observation contradicts assumptions that are fundamental to many models of surf zone dynamics and sediment transport. Analysis of a wider range of wave conditions is needed to assess the generality of these preliminary results. Using field data in the sediment transport model of Bailard (1981) suggests that both bed and suspended load are significant cross-shore transporting mechanisms on this low slope beach with moderate wave energy. Asymmetries in the oscillatory wave field tend to transport sediment shoreward, while the interaction of the offshore mean flow with waves produces an offshore sediment flux.

}, isbn = {0733-950X}, doi = {10.1061/(ASCE)0733-950X(1985)111:2(235)}, url = {Two commonly used methods of simulating random time series, given a target power spectrum, are discussed. Wave group statistics, such as the mean length of runs of high waves, produced by the different simulation schemes are compared. The target spectra used are obtained from ocean measurements, and cover a wide range of ocean conditions. For a sufficiently large number of spectral components, no significant differences are found in the wave group statistics produced by the two simulation techniques.

}, isbn = {0141-1187}, doi = {10.1016/0141-1187(85)90039-2}, url = {A two-dimensional numerical model is used to predict the shoaling and breaking of surface gravity waves, and the resulting longshore currents, for 5 days of the Nearshore Sediment Transport Study Santa Barbara experiment. Data with incident waves having narrow-banded frequency and directional spectra are selected for comparison in accord with the model assumptions of unidirectional and monochromatic waves. The rms wave height is used for expressing wave energy in the calculations. The current model includes bottom friction, lateral mixing, and nonliner convective accelerations. The extensive field measurements of waves, including quantitative directional information, and longshore current distributions are used to test the model results. The predicted rms wave heights are consistent with the measurements. By tuning the model with field data of longshore currents, the comparison between the model and data shows good agreement, and the obtained values of free parameters are relatively constant for the five experiment days.

}, doi = {10.1029/JC090iC03p04951}, url = {A data-adaptive directional-spectrum estimator is developed for {\textquotedblleft}point{\textquotedblright} measurement systems such as the pitch and roll buoy and slope array. This estimator, unlike the much employed unimodal cosine power parameterization method of Longuet-Higgins and others, does not make a priori assumptions about the shape of the directional spectrum. Instead improved resolution is obtained with a maximum likelihood method similar to those successfully used with spatial arrays. The numerical algorithm is relatively simple and computationally fast. The capabilities and limitations of the new estimator are illustrated with a variety of synthetic directional spectra. The estimator is applied to field data obtained from a slope array in 9 m depth at Santa Barbara, California and is found to yield physically realistic directional spectra. It marginally resolves two directional modes that topographical features dictate should be separated by approximately 70 degrees.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1984)014<1800:adaowd>2.0.co;2}, url = {Wave group statistics predicted by linear theories are compared to numerical simulations, thus determining ranges of spectral shapes for which the theories are valid. It is found that these theories are not generally valid for ocean data because of many assumptions and simplifications beyond linearity and random phase or because their range of applicability does not include the vast majority of ocean conditions. The simulations also provide quantitative information about the variability of linear wave group statistics which is useful when examining ocean field data. The simulation technique is used to show that important ocean gravity wave group statistics are not inconsistent with an underlying wave field composed of linearly superposed random waves. The majority of the field data examined were collected in 10 m depth; significant wave heights varied from about 20 to 200 cm, and the spectral shapes ranged from fairly narrow to broad (1

}, doi = {10.1029/JC089iC03p03623}, url = {A field experiment is used to evaluate a numerical model of the sheltering of gravity waves by islands offshore of the Southern California region. The sheltering model considered here includes only the effects of island blocking and wave refraction over the island bathymetry. Wave frequency and directional spectra measured in the deep ocean (unsheltered region west of the islands) were used as input to the sheltering model and compared with coastal observations. An airborne L-band synthetic aperture radar was used to image the directional properties of the waves in the deep ocean. In addition to the unsmoothed spectra, a unimodal directional spectrum model obtained from fits to the radar spectra was also employed to suppress the high noise level of this system. Coastal measurements were made in about 10 m depth at Torrey Pines Beach with a high resolution array of pressure sensors. The model predictions and data at Torrey Pines Beach agree well in a limited frequency range (0.082 to 0.114 Hz) where the unimodal deep ocean model is appropriate. The prediction that unimodal northern swell in the deep ocean results in a bimodal directional spectrum at Torrey Pines Beach is quantitatively verified. The northern peak of the bimodal spectra is due to waves coming through the window between San Clemente and San Miguel-Santa Rosa Islands. The southerly peak is due to wave refraction over Cortez and Tanner Banks. For lower frequency waves, the effects of strong refraction in the island vicinity are shown qualitatively. Refraction can theoretically supply up to approximately 10\% of the deep ocean energy that is otherwise blocked at this site. The modifications of the island shadows due to wave refraction become theoretically negligible for wave frequencies 0.11Hz. Also, local wave generation effects, which are not included in this sheltering model, are shown to be occasionally important for waves with frequencies 0.12Hz.

}, isbn = {0278-4343}, doi = {10.1016/0278-4343(84)90042-6}, url = {Field experiments have been performed to evaluate and intercompare two techniques for measuring run-up on natural beaches, resistance wires and films. Simultaneous deployment of wire sensors shows a low error (\< 5\%) in electronics gain, but a strong sensitivity to the elevation of the wires above the beach face. On a low slope (β \~{} 0.02) beach, with incident wind waves of moderate height (H \~{} 1 m), differences of only a few cm in the wire elevation cause variance differences as large as 25\%, in otherwise identical sensors. Replicate digitizations of the same run-up film show variance differences as large as 20\%, with an average deviation from the mean variance of 8\%.Use of the film and resistance wire sensors on the same run-up field showed small differences in the mean swash elevation (i.e., set-up), but an 83\% difference in swash variance. Much further work is needed to determine the dependence of sensor differences on beach slope, porosity, camera elevation and other factors.

}, isbn = {0378-3839}, doi = {10.1016/0378-3839(84)90008-5}, url = {Two nonlinear models that describe the shoaling of unidirectional surface gravity waves are developed. Based on variants of Boussinesq{\textquoteright}s equations, the models are cast as a set of coupled evolution equations for the amplitudes and phases of the temporal Fourier modes of the wave field. Triad interactions across the entire wind--wave frequency band (0.05-0.25 Hz) provide the mechanism for cross spectral energy transfers and modal phase modifications as the waves propagate shoreward through the shoaling region (10-3 m depth). A field experiment, designed to test the operational validity of the nonlinear shoaling models, provided data on wave parameters over a wide range of conditions. Three representative data sets illustrating different initial spectral shapes and subsequent evolutions are compared with predictions of the nonlinear shoaling models and linear, finite-depth theory. Power spectral comparisons, as well as spectra of coherence and relative phase between model predictions and data, indicate that the nonlinear models accurately predict Fourier coefficients of the wave field through the shoaling region for all data sets. Differences between the predictions of the various models are related to differences in the models{\textquoteright} dispersion relations. Although generally inferior to the nonlinear models, linear, finite-depth theory accurately predicts Fourier coefficients in regions of physical and frequency space where nonlinear evolution of the power spectrum is not observed, thus verifying the validity of the linear, finite-depth dispersion relation in limited portions of physical and frequency space in the shoaling region.

}, doi = {10.1098/rsta.1984.0019}, url = {The radiation stresses Sij associated with the propagation of wind-generated waves are principal driving forces for several important surf-zone processes. The accurate estimation of the onshore flux of longshore-directed mean momentum Syx, using a linear array of pressure sensors, is considered here. Three analysis methods are examined: integration of two high-resolution directional-spectrum estimators [maximum likelihood (MLM) and a modified version (IMLM)], and a direct estimator of the Syx directional moment (DMMv) which is developed here.The Syx estimation methods are compared using numerical simulations and field data from two experiments at Torrey Pines Beach, California. In the first field experiment, IMLM and DMM, estimates of Syx (from a 3-element, 99 m long linear array) showed excellent agreement with a slope array (Higgins et al., 1981) in the frequency range 0.05{\textendash}0.15 Hz. In the second experiment, IMLM and DMM, estimates of Syx (from a 5-element, 360 m long array) agreed with values of Syx obtained from a nearby orthogonal-axis current meter for the frequency range 0.06{\textendash}0.11 Hz. The integration of the MLM directional spectrum estimates yields biased (low) values of Syx. Although the DMM method is used here for the estimation of Syx, it can easily be adapted for the calculation of any arbitrary directional moment. While conventional methods are shown to be deficient in Syx estimation, they provide accurate estimates of Sxx, the onshore flux of onshore-directed momentum.

}, isbn = {0022-3670}, doi = {10.1175/1520-0485(1983)013<1698:rse>2.0.co;2}, url = {The transformation of random wave heights during shoaling, including waves breaking in the surf zone, was measured with an extensive array of instruments in the field. The initially Rayleigh height distributions in 10-m depth were observed to be modified by shoaling and breaking into new distributions which are again nearly Rayleigh but with some energy loss. Using locally measured Hrms, the Rayleigh distribution describes the measured central moments of H1/3 and H1/10 with average errors of -0.2\% and -1.8\%, respectively. The Rayleigh distribution is used to describe the random nature of wave heights in a single-parameter transformation model based on energy flux balance. The energy losses associated with wave breaking are parameterized using observed breaking wave distributions coupled with a periodic bore dissipation model. Using incident waves measured in 10-m depth as input conditions, the model predicts Hrms at shoreward locations within a rms error of {\textpm}9\%. The single free parameter of the model, a constant B representing the fraction of foam on the face of a wave, was chosen to best fit the data. The resulting large value of B implies that the simple periodic bore dissipation function substantially underestimates the actual dissipation.

}, isbn = {0148-0227}, doi = {10.1029/JC088iC10p05925}, url = {Pressure and horizontal current (u, v) time series were measured at different positions across the inner 150 m of a wide (≈500 m) surf zone of a microtidal high wave-energy beach. Incident waves had average heights of 3{\textendash}4 m with maxima of 5 m and periods of 12 to 15 sec. Bores of broken waves diminished in height at a nearly constant rate as they progressed across the surf zone. The ratio, γ, of bore height H to local water depth h was everywhere less than 1 for even the highest bores and was on the order of 0.40 for the significant bores at incident wave frequencies. Rip circulation was weak or absent but a moderate longshore current was present. Shore-normal flows were vertically segregated with strong net onshore flows prevailing just below the surface accompanied by weaker net seaward flows near the bed. Spectra of water surface oscillations, η as determined from pressure, u, and v reveal that most of the energy in the inner surf zone was at infragravity frequencies (periods greater than 30 sec). Shoreward decay of wave energy at incident wave frequencies was accompanied by shoreward growth of infragravity energy. Near the beach the infragravity oscillations had heights on the order of 1 m. Cross-spectra show that the infragravity oscillations were standing in the shore-normal direction. From the relative magnitudes of infragravity versus incident wave currents, it is inferred that the surf beat may be an order of magnitude more important than incident waves to the transport of sediment in the inner surf zone.

}, isbn = {0025-3227}, doi = {10.1016/0025-3227(82)90179-7}, url = {Field measurements of wave height and speed from 7-m depth shoreward are described. The experiment plan consisted of a shore-normal transect of closely spaced (compared to a dominant wave length) velocity, pressure, and elevation sensors on an almost plane profile having an inshore slope of 1:50. As the waves shoal and begin to break, the dominant dissipative mechanism is due to turbulence generated at the crest, and wave heights become increasingly depth controlled as they progress across the surf zone. Wave heights in the inner surf zone are strongly depth dependent; the envelope of the wave heights is described by Hrms = 0.42 h. The depth dependence of the breaking wave height is shown to be related to the kinematic instability criterion. Celerity spectra were measured by using phase spectra calculated between pairs of adjacent sensors. Inshore of 4-m depth, the celerity was found distant over the energetic region of the spectrum. A {\textquoteleft}mean{\textquoteright} celerity was compared with linear theory and was within +20\% and -10\%, showing good agreement for such a nonlinear, dissipative region.

}, isbn = {0148-0227}, doi = {10.1029/JC087iC12p09499}, url = {Genetically, there are two types of beach cusps; those formed in the surfzone by the nearshore circulation system, and those formed on the beachface by the swash and backwash. The latter are here called {\textquotedblleft}swash{\textquotedblright} cusps, and a simple model relating the physical dimensions of swash cusps to the properties of the incident wave field and the mean beach slope is developed. As in some previous models, the cusp wavelength is controlled by the longshore wavelength of edge waves, but the edge waves are now required only to provide small periodic perturbations on an originally uniform beach. Further cusp growth occurs because of the interactions between the incident waves and the perturbed topography. The maximum cusp height (apex to valley) is hypothesized to be proportional to the significant vertical excursion of swash motions. It follows from the above assumptions that the maximum possible cusp steepness (cusp height/cusp longshore wavelength) is proportional to the mean on-offshore beach slope. This result agrees with field data, and the value of the ratio of maximum cusp height to beach slope differs from that obtained theoretically by Guza and Bowen (1981) using a complicated non-linear model with rather different physics. The present model implies that edge waves, although necessary for initiating the initial bedform perturbation, need not persist for the development of mature cusp topography.

}, isbn = {0025-3227}, doi = {10.1016/0025-3227(82)90033-0}, url = {Run-up (swash) oscillations were measured on a gently sloping beach face for a variety of incident wave conditions. Run-up energy spectra at wind wave frequencies show an {\textflorin}-3 dependence and energy levels that are independent of incident wave height. This suggests saturation. In contrast, run-up energy at surf beat periods increase approximately linearly with increasing incident wave energy. Thus, in the inner surf zone, where wave breaking limits the energy at wind wave frequencies, the principal manifestation of large incident wind waves is energetic surf beat.

}, isbn = {0148-0227}, doi = {10.1029/JC087iC01p00483}, url = {Measurements of wave elevation and orbital velocity in the shoaling, breaking, and bore regime of single-frequency laboratory waves show that third-order Stokes theory, when energy flux is conserved, predicts the wave height change and harmonic growth in the regime where the Ursell number Ur = (H/ h)/(kh)2 is 0(1) or less. Shoreward of the Stokes region and up to the breakpoint, harmonic amplitudes are well described by the cnoidal theory. It is shown theoretically that a smooth transition regime exists between Stokes and cnoidal regions for waves which eventually break by plunging. The wave profile asymmetry about the vertical plane observed in near-breaking waves and bores is due to slow changes of phase of the harmonics relative to the primary wave as the wave train shoals. By contrast, only asymmetry about the horizontal plane is possible in the Stokes and cnoidal wave theories, since these classical solutions allow no relative phase shifts between harmonics. Velocity measurements made with hot-film anemometers show that {\textquoteleft}unorganized{\textquoteright} fluctuations at the bottom under breaking waves are of the order of half the rms amplitude of the wave-induced {\textquoteleft}organized{\textquoteright} flow. The correlation between surface elevation and bottom velocity under breakers and bores suggests that turbulence contributes more strongly to the unorganized flow at the bottom under plunging than under spilling waves.

}, isbn = {0148-0227}, doi = {10.1029/JC086iC05p04149}, url = {Nineteen biaxial electromagnetic current meters have been used to determine the longshore and on/offshore structure of currents at surf beat periods (1{\textendash}4 min). The sensors formed two linear arrays, a long-shore array within the surf zone and an on/offshore array stretching from the shoreline to well beyond the breaker line. Analysis of the longshore current components yields a clear picture of progressive low-mode edge waves, with frequency-wave number dispersion relations which are in remarkably good agreement with predictions. Some separation of edge wave modes is found, with mode zero energy dominating in the frequency band 0.006 and 0.011 Hz and mode one between 0.015 and 0.025 Hz. On/offshore currents present a rather different picture which, while not inconsistent with the longshore currents, suggests that other sources of energy are also important to the on/offshore currents. These include standing edge waves probably formed by reflections at nearby Scripps Canyon, and motions which are nonresonantly forced by incoming wave groups.

}, isbn = {0148-0227}, doi = {10.1029/JC086iC07p06451}, url = {There is increasing evidence from field observations that beach cusps are often formed by subharmonic edge waves, edge waves which are generated by an instability in the incoming wind waves. A theoretical analysis suggests that the changing beach topography as the cusps grow provides a negative feedback to the excitation of the subharmonic edge waves. As the cusps grow, the edge waves subside. A maximum cusp amplitude is calculated, based on the assumption that some edge wave activity must persist to maintain the cusps. The theoretical prediction that cusp amplitude will increase with increasing beach slope and increasing incident wave period is in agreement with the trends suggested by some of the more detailed field observations of beach cusps.

}, isbn = {0148-0227}, doi = {10.1029/JC086iC05p04125}, url = {Wave set-up, the superelevation of mean water level owing to the presence of breaking incident waves, was measured at the shoreline of a natural beach. Offshore pressure sensors monitored incident wave conditions. The set-up of the shoreline was found to be about 0.17Hs,$\infty$, where Hs$\infty$ is the significant wave height in deep water.

}, isbn = {0148-0227}, doi = {10.1029/JC086iC05p04133}, url = {Sea surface elevations, or pressures, and velocities were measured at closely spaced (wavelength or less) locations in a line extending from 10-m depth to inside the surf zone at Torrey Pines Beach, San Diego, California. Intercomparisons of local pressure, velocity, and sea surface elevation spectra for the wind wave frequencies (0.05{\textendash}0.3 Hz) were made by using linear wave theory. Errors in both total variance and energy density in a particular frequency band are less than 20\% both inside and outside the surf zone, except in the immediate vicinity of the breakpoint, where larger disparities are observed. Surface elevation spectra calculated at 10 m were shoaled by using linear wave theory. The total variance of stations between 10- and 3-m depth are typically predicted with less than 20\% error, although harmonic amplification and other nonlinear effects can lead to significant errors in the prediction at particular frequency bands. Observations inside 3-m depth significantly departed from the predictions of linear shoaling theory.

}, isbn = {0148-0227}, doi = {10.1029/JC085iC03p01524}, url = {Monochromatic waves obliquely incident on a plane beach, and strongly reflected there, are unstable to perturbations by edge waves. Theory suggests the possible width of the resonant edge wave frequency band. Experiments on beaches with absorbers at both ends show that the excited waves have frequencies at the centre of the band, as predicted by Guza \& Bowen (1975). Advection by mean longshore currents must be taken into account. If reflectors are placed at the beach ends, the additional boundary conditions apparently lead to resonances scattered across the resonant band.

}, isbn = {0022-1120}, doi = {10.1017/s0022112079001427}, url = {Surf beat, wave motion at relatively low frequency (periods of 30{\textendash}200 s), is often observed on beaches. However, even with modern instrumentation it is difficult to describe the spatial variation of the low-frequency motion; consequently, the relative importance of a number of suggestions which, at least in theory, provide mechanisms for the generation of low-frequency energy has never been established. Recent observations (e.g., Huntley, 1976) have reinforced the idea that edge waves, the free wave modes trapped at the shoreline, are a major component of low-frequency energy. One of the most interesting explanations of surf beat suggests that the beating between particular pairs of incoming waves leads to resonant growth of edge wave modes, which may then dominate the low-frequency spectrum (Gallagher, 1971). Empirical evidence is essential, as any theoretical development breaks down when the incoming waves break, a fundamental problem with Gallagher{\textquoteright}s (1971) model. To investigate the importance of this resonant interaction, the general interaction conditions were therefore used to design laboratory experiments in which both resonant and nonresonant conditions were expected. The experimental results show that the response at the beat frequency is stronger when the resonance conditions for edge wave growth are satisfied and that the response is in the form of the theoretically predicted edge wave mode, even when the incident waves are breaking. These results strongly suggest that surf beat is predominantly an edge wave phenomenon.

}, isbn = {0148-0227}, doi = {10.1029/JC083iC04p01913}, url = {Time series of shoreline run-up on two natural beaches have been measured by using a time-lapse camera. Spectra of these time series and two other run-up spectra measured by Suhayda (1972) suggest that for the frequency band over which incident waves are large enough to break a universal {\textquoteleft}saturation{\textquoteright} form for the vertical run-up spectrum occurs, with energy density E({\textflorin}) = [∈{\textasciicircum}csgβ2/(2π{\textflorin})2]2, where g is the gravitational acceleration, β is the beach slope, and {\textflorin} is the frequency (in hertz). Parameter ∈{\textasciicircum}cs(Δ{\textflorin}){\textonehalf} is a universal nondimensional constant, found to have a value of about 1, where Δ{\textflorin} is the bandwidth over which incident waves are large enough to break in the surf zone. This result is discussed in relation to previous laboratory experiments and theories, based on monochromatic waves, which suggest the existence of a limiting amplitude for standing waves formed by reflection at the shoreline. This limiting amplitude is related to a critical parameter ∈cs by a = ∈csgβ2/(2π{\textflorin})2. A possible interpretation of ∈{\textasciicircum}cs(Δ{\textflorin}){\textonehalf} in terms of ∈cs is given based on percentage exceedances of the critical downslope acceleration gβ2. In this interpretation we have assumed a Gaussian distribution for run-up acceleration. This assumption cannot be tested directly, but the observed distribution functions for run-up elevation suggest that it may need to be modified. Departures from the universal spectrum athigher and lower frequencies are briefly discussed.

}, isbn = {0148-0227}, doi = {10.1029/JC082i018p02577}, url = {Genetically, beach cusps are of at least two types: those linked with incident waves which are surging and mostly reflected (reflective systems) and those generated on beaches where wave breaking and nearshore circulation cells are important (dissipative systems). The spacings of some cusps formed under reflective wave conditions both in the laboratory and in certain selected natural situations are shown to be consistent with models hypothesizing formation by either (1) subharmonic edge waves (period twice that of the incident waves) of zero mode number or (2) synchronous (period equal to that of incident waves) edge waves of low mode. Experiments show that visible subharmonic edge wave generation occurs on nonerodable plane laboratory beaches only when the incident waves are strongly reflected at the beach, and this observation is quantified. Edge wave resonance theory and experiments suggest that synchronous potential edge wave generation can also occur on reflective beaches and is a higher-order, weaker resonance than the subharmonic type. In dissipative systems, modes of longshore periodic motion other than potential edge waves may be important in controlling the longshore scale of circulation cells and beach morphologies. On reflective plane laboratory beaches, initially large subharmonic edge waves rear-rage sand tracers into shapes which resemble natural beach cusps, but the edge wave amplitudes decrease as the cusps grow. Cusp growth is thus limited by negative feedback from the cusps to the edge wave excitation process. Small edge waves can form longshore periodic morphologies by providing destabilizing perturbations on a berm properly located in the swash zone. In this case the retreating incident wave surge is channelized into breeches in the berm caused by the edge waves, and there is an initially positive feedback from the topography to longshore periodic perturbations.

}, isbn = {0148-0227}, doi = {10.1029/JC080i021p02997}, url = {A monochromatic unidirectional wave train, incident on a plane beach and strongly reflected there, is shown to transfer energy to edge waves of lower frequency through a weak nonlinear interaction. For any angle of wave incidence the most readily excited edge wave perturbation consists of two low-mode progressive edge waves, generally having different frequencies and wave numbers, traveling in opposite directions along the beach. Standing edge waves, which might form stationary morphologic features with a regular longshore rhythm, are theoretically only excited when the primary surface waves are normally incident. However, edge waves generated by almost normally incident primary waves may be linked to features which slowly migrate along shore. On beaches bounded by headlands or jetties the progressive edge waves excited would be reflected at both ends, forming a complex pattern of standing waves. For beaches bounded at one end, only one of the edge waves would be standing. Regular beach cusps would therefore be expected in the vicinity of barriers. These cusps should decrease in relief with increasing distance from the obstacle as the reflected edge wave, which is not being actively forced, dies away due to viscous dissipation and further nonlinear interactions. Intriguingly, the cusps should have slightly different wavelengths on either side of the obstacle.

}, isbn = {0148-0227}, doi = {10.1029/JC080i033p04529}, url = {It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth{\textquoteright}s rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann{\textquoteright}s (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.

}, isbn = {0148-0227}, doi = {10.1029/JC079i009p01285}, url = {