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Fiedler, JW, Smit PB, Brodie KL, McNinch J, Guza RT.  2019.  The offshore boundary condition in surf zone modeling. Coastal Engineering. 143:12-20.   10.1016/j.coastaleng.2018.10.014   AbstractWebsite

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.

Gallien, TW, O'Reilly WC, Flick RE, Guza RT.  2015.  Geometric properties of anthropogenic flood control berms on southern California beaches. Ocean & Coastal Management. 105:35-47.   10.1016/j.ocecoaman.2014.12.014   AbstractWebsite

Coastal flood riskfrom coincident high tides' 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.

Spydell, MS, Feddersen F, Guza RT, MacMahan J.  2014.  Relating Lagrangian and Eulerian horizontal eddy statistics in the surfzone. Journal of Geophysical Research-Oceans. 119:1022-1037.   10.1002/2013jc009415   AbstractWebsite

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'' to "frozen-field'' [Lumpkin et al., 2002], although conclusions are limited by the statistical sampling errors in both T-L/T-A and V/sigma.

Young, AP, Guza RT, Dickson ME, O'Reilly WC, Flick RE.  2013.  Ground motions on rocky, cliffed, and sandy shorelines generated by ocean waves. Journal of Geophysical Research-Oceans. 118:6590-6602.   10.1002/2013jc008883   AbstractWebsite

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.

Feddersen, F, Clark DB, Guza RT.  2011.  Modeling surf zone tracer plumes: 1. Waves, mean currents, and low-frequency eddies. Journal of Geophysical Research-Oceans. 116   10.1029/2011jc007210   AbstractWebsite

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.

Gorrell, L, Raubenheimer B, Elgar S, Guza RT.  2011.  SWAN predictions of waves observed in shallow water onshore of complex bathymetry. Coastal Engineering. 58:510-516.   10.1016/j.coastaleng.2011.01.013   AbstractWebsite

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.

Clark, DB, Feddersen F, Guza RT.  2010.  Cross-shore surfzone tracer dispersion in an alongshore current. Journal of Geophysical Research-Oceans. 115   10.1029/2009jc005683   AbstractWebsite

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.

Yates, ML, Guza RT, O'Reilly WC, Seymour RJ.  2009.  Seasonal persistence of a small southern California beach fill. Coastal Engineering. 56:559-564.   10.1016/j.coastaleng.2008.11.004   AbstractWebsite

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'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.

Apotsos, A, Raubenheimer B, Elgar S, Guza RT.  2008.  Wave-driven setup and alongshore flows observed onshore of a submarine canyon. Journal of Geophysical Research-Oceans. 113   10.1029/2007jc004514   AbstractWebsite

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.

Thomson, J, Elgar S, Raubenheimer B, Herbers THC, Guza RT.  2006.  Tidal modulation of infragravity waves via nonlinear energy losses in the surfzone. Geophysical Research Letters. 33   10.1029/2005gl025514   AbstractWebsite

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.

Raubenheimer, B, Elgar S, Guza RT.  2004.  Observations of swash zone velocities: A note on friction coefficients. Journal of Geophysical Research-Oceans. 109   10.1029/2003jc001877   AbstractWebsite

[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).

Herbers, THC, Orzech M, Elgar S, Guza RT.  2003.  Shoaling transformation of wave frequency-directional spectra. Journal of Geophysical Research-Oceans. 108   10.1029/2001jc001304   AbstractWebsite

[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.

Sheremet, A, Guza RT, Elgar S, Herbers THC.  2002.  Observations of nearshore infragravity waves: Seaward and shoreward propagating components. Journal of Geophysical Research-Oceans. 107   10.1029/2001jc000970   AbstractWebsite

[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.

Herbers, THC, Elgar S, Sarap NA, Guza RT.  2002.  Nonlinear dispersion of surface gravity waves in shallow water. Journal of Physical Oceanography. 32:1181-1193.   10.1175/1520-0485(2002)032<1181:ndosgw>;2   AbstractWebsite

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.

Noyes, TJA, Guza RT, Elgar S, Herbers THC.  2002.  Comparison of methods for estimating nearshore shear wave variance. Journal of Atmospheric and Oceanic Technology. 19:136-143.   10.1175/1520-0426(2002)019<0136:comfen>;2   AbstractWebsite

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.

Elgar, S, Gallagher EL, Guza RT.  2001.  Nearshore sandbar migration. Journal of Geophysical Research-Oceans. 106:11623-11627.   10.1029/2000jc000389   AbstractWebsite

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.

Herbers, THC, Elgar S, Guza RT.  1999.  Directional spreading of waves in the nearshore. Journal of Geophysical Research-Oceans. 104:7683-7693.   10.1029/1998jc900092   AbstractWebsite

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'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.

Feddersen, F, Guza RT, Elgar S, Herbers THC.  1998.  Alongshore momentum balances in the nearshore. Journal of Geophysical Research-Oceans. 103:15667-15676.   10.1029/98jc01270   AbstractWebsite

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.

Chen, YZ, Guza RT, Elgar S.  1997.  Modeling spectra of breaking surface waves in shallow water. Journal of Geophysical Research-Oceans. 102:25035-25046.   10.1029/97jc01565   AbstractWebsite

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.

Elgar, S, Guza RT, Freilich MH, Briggs MJ.  1992.  Laboratory Simulations of Directionally Spread Shoaling Waves. Journal of Waterway Port Coastal and Ocean Engineering-Asce. 118:87-103.   10.1061/(asce)0733-950x(1992)118:1(87)   AbstractWebsite

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.