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Deike, L, Pizzo N, Melville WK.  2017.  Lagrangian transport by breaking surface waves. Journal of Fluid Mechanics. 829:364-391.   10.1017/jfm.2017.548   AbstractWebsite

The Lagrangian transport due to non-breaking and breaking focusing wave packets is examined. We present direct numerical simulations of the two-phase air-water Navier-Stokes equations describing focusing wave packets, investigating the Lagrangian drift by tracking tracer particles in the water before, during and after the breaking event. The net horizontal transport for non-breaking focusing packets is well described by the classical Stokes drift, both at the surface and in the bulk of the fluid, where the e-folding scale of the evanescent vertical profile is given by the characteristic wavenumber. For focusing wave packets that lead to breaking, we observe an added drift that can be ten times larger than the classical Stokes drift for a non-breaking packet at the surface, while the initial depth of the broken fluid scales with the wave height at breaking. We find that the breaking induced Lagrangian transport scales with the breaking strength. A simple scaling argument is proposed to describe this added drift and is found to be consistent with the direct numerical simulations. Applications to upper ocean processes are discussed.

Deike, L, Lenain L, Melville WK.  2017.  Air entrainment by breaking waves. Geophysical Research Letters. 44:3779-3787.   10.1002/2017gl072883   AbstractWebsite

We present an estimate of the total volume of entrained air by breaking waves in the open ocean, based on a model for a single breaking wave and the statistics of breaking waves measured in the field and described by the average length of breaking crests moving with speeds in the range (c,c + dc) per unit area of ocean surface, Lambda(c)dc, introduced by Phillips (1985). By extending the single breaking wave model to the open ocean, we show that the volume flux of air entrained by breaking waves, V-A (volume per unit ocean area per unit time, a velocity), is given by the third moment of Lambda(c), modulated by a function of the wave slope. Using field measurements of the distribution Lambda(c) and the wave spectrum, we obtain an estimate of the total volume flux of air entrained by breaking for a wide range of wind and wave conditions. These results pave the way for accurate remote sensing of the air entrained by breaking waves and subsequent estimates of the associated gas transfer. Plain Language Summary Processes at the ocean-atmosphere interface control the transfer of gas and have a profound effect on weather and climate. Among these processes, breaking waves play an important role by entraining bubbles into the ocean. The dynamics and statistics of breaking waves in a particular location of the ocean are complex and depend mainly on the local sea state and not only the wind speed. However, current parameterizations of air-sea gas transfer rely solely on the wind speed, which leads to large uncertainties in the air-sea exchange budget of gases key to the climate system. In this paper, we present a theoretical model to estimate the volume of air entrained in the ocean by breaking waves. Using our model and field measurements of the wave and wave breaking statistics, we obtain an estimate of the total volume of air entrained by breaking for a wide range of wind and wave conditions. These results pave the way for accurate remote sensing of the air entrained by breaking waves and estimates of the associated gas transfer, which will lead to improvements in current climate models.

Romero, L, Lenain L, Melville WK.  2017.  Observations of surface wave-current interaction. Journal of Physical Oceanography. 47:615-632.   10.1175/jpo-d-16-0108.1   AbstractWebsite

Wave-current interaction can result in significant inhomogeneities of the ocean surface wave field, including modulation of the spectrum, wave breaking rates, and wave statistics. This study presents novel airborne observations from two experiments: 1) the High-Resolution Air-Sea Interaction (HiRes) experiment, with measurements across an upwelling jet off the coast of Northern California, and 2) an experiment in the Gulf of Mexico with measurements of waves interacting with the Loop Current and associated eddies. The significant wave height and slope varies by up to 30% because of these interactions at both sites, whereas whitecap coverage varies by more than an order of magnitude. Whitecap coverage is well correlated with spectral moments, negatively correlated with the directional spreading, and positively correlated with the saturation. Surface wave statistics measured in theGulf ofMexico, including wave crest heights and lengths of crests per unit surface area, show good agreement with second-order nonlinear approximations, except over a focal area. Similarly, distributions of wave heights are generally bounded by the generalized Boccotti distribution, except at focal regions where the wave height distribution reaches the Rayleigh distribution with a maximum wave height of 2.55 times the significant wave height, which is much larger than the standard classification for extreme waves. However, theoretical distributions of spatial statistics that account for second-order nonlinearities approximately bound the observed statistics of extreme wave elevations. The results are discussed in the context of improved models of breaking and related air-sea fluxes.

Lenain, L, Melville WK.  2017.  Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer. Journal of Physical Oceanography. 47:69-84.   10.1175/jpo-d-16-0058.1   AbstractWebsite

Sea spray aerosols represent a large fraction of the aerosols present in the maritime environment. Despite evidence of the importance of surface wave- and wave breaking-related processes in coupling the ocean with the atmosphere, sea spray source generation functions are traditionally parameterized by the 10-m wind speed U-10 alone. It is clear that unless the wind and wave field are fully developed, the source function will be a function of both wind and wave parameters. This study reports primarily on the aerosol component of an air-sea interaction experiment, the phased-resolved High-Resolution Air-Sea Interaction Experiment (HIRES), conducted off the coast of northern California in June 2010. Detailed measurements of aerosol number concentration in the marine atmospheric boundary layer (MABL) at altitudes ranging from as low as 30 m up to 800 m above mean sea level (MSL) over a broad range of environmental conditions (significant wave height H-s of 2 to 4.5 m and U-10 from 10 to 18 m s(-1)) collected from an instrumented research aircraft are presented. Aerosol number densities and volume are computed over a range of particle diameters from 0.1 to 200 mu m, while the sea surface conditions, including H-s, moments of the breaker length distribution ?(c), and wave breaking dissipation, were measured by a suite of electro-optical sensors that included the NASA Airborne Topographic Mapper (ATM). The sea-state dependence of the aerosol concentration in the MABL is evident, stressing the need to incorporate wave parameters in the spray source generation functions that are traditionally parameterized by surface winds alone.

Bresnahan, PJ, Wirth T, Martz TR, Andersson AJ, Cyronak T, D’Angelo S, Pennise J, Melville KW, Lenain L, Statom N.  2016.  A sensor package for mapping pH and oxygen from mobile platforms. Methods in Oceanography. 17:1-13.   10.1016/j.mio.2016.04.004   Abstract

A novel chemical sensor package named “WavepHOx” was developed in order to facilitate measurement of surface ocean pH, dissolved oxygen, and temperature from mobile platforms. The system comprises a Honeywell Durafet pH sensor, Aanderaa optode oxygen sensor, and chloride ion selective electrode, packaged into a hydrodynamic, lightweight housing. The WavepHOx has been deployed on a stand-up paddleboard and a Liquid Robotics Wave Glider in multiple near-shore settings in the Southern California Bight. Integration of the WavepHOx into these mobile platforms has enabled high spatiotemporal resolution pH and dissolved oxygen data collection. It is a particularly valuable tool for mapping shallow, fragile, or densely vegetated ecosystems which cannot be easily accessed by other platforms. Results from three surveys in San Diego, California, are reported. We show pH and dissolved oxygen variability >0.3 and >50% saturation, respectively, over tens to hundreds of meters to highlight the degree of natural spatial variability in these vegetated ecosystems. When deployed during an extensive discrete sampling program, the WavepHOx pH had a root mean squared error of 0.028 relative to pH calculated from fifty six measurements of total alkalinity and dissolved inorganic carbon, confirming its capacity for accurate, high spatiotemporal resolution data collection.

Grare, L, Lenain L, Melville WK.  2016.  The influence of wind direction on Campbell Scientific CSAT3 and Gill R3-50 sonic anemometer measurements. Journal of Atmospheric and Oceanic Technology. 33:2477-2497.   10.1175/jtech-d-16-0055.1   AbstractWebsite

Measurements from the Campbell CSAT3 and Gill R3-50 anemometers were conducted in four different experiments, in laboratory and field environments. Consistent differences between these two sonic anemometers were observed. The data have revealed that the differences were strongly correlated with the wind direction. According to the datasets used, the CSAT3 was the anemometer whose measurements were more sensitive to the instrument's orientation relative to the wind direction. While the mean wind speed and direction remained within the manufacturers' specifications (a few percent for the wind speed and a few degrees for the wind direction), the estimates of the friction velocity from the CSAT3 differed from the R3-50 by up to 20%.

Pizzo, NE, Deike L, Melville WK.  2016.  Current generation by deep-water breaking waves. Journal of Fluid Mechanics. 803:275-291.   10.1017/jfm.2016.469   Abstract

We examine the partitioning of the energy transferred to the water column by deep-water wave breaking; in this case between the turbulent and mean flow. It is found that more than 95 % of the energy lost by the wave field is dissipated in the first four wave periods after the breaking event. The remaining energy is in the coherent vortex generated by breaking. A scaling argument shows that the ratio between the energy in this breaking generated mean current and the total energy lost from the wave field to the water column due to breaking scales as (hk)(1/2), where hk is the local slope at breaking. This model is examined using direct numerical simulations of breaking waves solving the full two-phase air-water Navier-Stokes equations, as well as the limited available laboratory data, and good agreement is found for strong breaking waves.

Reineman, BD, Lenain L, Melville WK.  2016.  The use of ship-launched fixed-wing UAVs for measuring the marine atmospheric boundary layer and ocean surface processes. Journal of Atmospheric and Oceanic Technology. 33:2029-2052.   10.1175/jtech-d-15-0019.1   AbstractWebsite

The deployment and recovery of autonomous or remotely piloted platforms from research vessels have become a way of significantly extending the capabilities and reach of the research fleet. This paper describes the use of ship-launched and ship-recovered Boeing-Insitu ScanEagle unmanned aerial vehicles (UAVs). The UAVs were instrumented to characterize the marine atmospheric boundary layer (MABL) structure and dynamics, and to measure ocean surface processes during the October 2012 Equatorial Mixing (EquatorMix) experiment in the central Pacific and during the July 2013 Trident Warrior experiment off the Virginia coast. The UAV measurements, including atmospheric momentum and radiative, sensible, and latent heat fluxes, are complemented by measurements from ship-based instrumentation, including a foremast MABL eddy-covariance system, lidar altimeters, and a digitized X-band radar system. During EquatorMix, UAV measurements reveal longitudinal atmospheric roll structures not sampled by ship measurements, which contribute significantly to vertical fluxes of heat and momentum. With the nadir-looking UAV lidar, surface signatures of internal waves are observed, consistent and coherent with measurements from ship-based X-band radar, a Hydrographic Doppler Sonar System, and a theoretical model. In the Trident Warrior experiment, the instrumented UAVs were used to demonstrate real-time data assimilation of meteorological data from UAVs into regional coupled ocean-atmosphere models. The instrumented UAVs have provided unprecedented spatiotemporal resolution in atmospheric and oceanographic measurements in remote ocean locations, demonstrating the capabilities of these platforms to extend the range and capabilities of the research fleet for oceanographic and atmospheric studies.

Pizzo, NE, Melville WK.  2016.  Wave modulation: the geometry, kinematics, and dynamics of surface-wave packets. Journal of Fluid Mechanics. 803:292-312.   10.1017/jfm.2016.473   AbstractWebsite

We examine the geometry, kinematics, and dynamics of weakly nonlinear narrow-banded deep-water wave packets governed by the modified nonlinear Schrodinger equation (Dysthe, Proc. R. Soc. Load. A., vol. 369, 1979, pp. 105-114; MNLSE). A new derivation of the spatial MNLSE, by a direct application of Whitham's method, elucidates its variational structure. Using this formalism, we derive a set of conserved quantities and moment evolution equations. Next, by examining the MNLSE in the limit of vanishing linear dispersion, analytic solutions can be found. These solutions then serve as trial functions, which when substituted into the moment evolution equations form a closed set of equations, allowing for a qualitative and quantitative examination of the MNLSE without resorting to numerically solving the full equation. To examine the theory we consider initially symmetric, chirped and unchirped wave packets, chosen to induce wave focusing and steepening. By employing the ansatz for the trial function discussed above, we predict, a priori, the evolution of the packet. It is found that the speed of wave packets governed by the MNLSE depends on their amplitude, and in particular wave groups speed up as they focus. Next, we characterize the asymmetric growth of the wave envelope, and explain the steepening of the forward face of the initially symmetric wave packet. As the packet focuses, its variance decreases, as does the chirp of the signal. These theoretical results are then compared with the numerical predictions of the MNLSE, and agreement for small values of fetch is found. Finally, we discuss the results in the context of existing theoretical, numerical and laboratory studies.

Deike, L, Melville WK, Popinet S.  2016.  Air entrainment and bubble statistics in breaking waves. Journal of Fluid Mechanics. 801:91-129.   10.1017/jfm.2016.372   AbstractWebsite

We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial scaling arguments. The air entrainment properties and bubble size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N(r,t)=B(V-0/2(pi))(epsilon(t- Delta tau)/Wg)r(-10/3) r(m)(-2/3) during the active breaking stages, where epsilon(t-Delta tau) is the time-dependent turbulent dissipation rate, with Delta tau the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r(m) the maximum bubble radius, g gravity, V-0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described by (N) over bar (r)=B(1/2 pi)(epsilon L-l(c)/Wg rho)r(-10/3)r(m)(-2/3), where epsilon(l) is the wave dissipation rate per unit length of breaking crest, rho the water density and L-c the length of breaking crest. Finally, the averaged total volume of entrained air, (V) over bar, per breaking event can be simply related to epsilon(l) by (V) over bar = B(epsilon L-l(c)/Wg rho), which leads to a relationship for a characteristic slope, S, of (V) over bar proportional to S-5/2. We propose a phenomenological turbulent bubble break-up model based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

Melville, WK, Lenain L, Cayan DR, Kahru M, Kleissl JP, Linden PF, Statom NM.  2016.  The Modular Aerial Sensing System. Journal of Atmospheric and Oceanic Technology. 33:1169-1184.   10.1175/jtech-d-15-0067.1   AbstractWebsite

Satellite remote sensing has enabled remarkable progress in the ocean, earth, atmospheric, and environmental sciences through its ability to provide global coverage with ever-increasing spatial resolution. While exceptions exist for geostationary ocean color satellites, the temporal coverage of low-Earth-orbiting satellites is not optimal for oceanographic processes that evolve over time scales of hours to days. In hydrology, time scales can range from hours for flash floods, to days for snowfall, to months for the snowmelt into river systems. On even smaller scales, remote sensing of the built environment requires a building-resolving resolution of a few meters or better. For this broad range of phenomena, satellite data need to be supplemented with higher-resolution airborne data that are not tied to the strict schedule of a satellite orbit. To address some of these needs, a novel, portable, high-resolution airborne topographic lidar with video, infrared, and hyperspectral imaging systems was integrated. The system is coupled to a highly accurate GPS-aided inertial measurement unit (GPS IMU), permitting airborne measurements of the sea surface displacement, temperature, and kinematics with swath widths of up to 800 m under the aircraft, and horizontal spatial resolution as low as 0.2 m. These data are used to measure ocean waves, currents, Stokes drift, sea surface height (SSH), ocean transport and dispersion, and biological activity. Hydrological and terrestrial applications include measurements of snow cover and the built environment. This paper describes the system, its performance, and present results from recent oceanographic, hydrological, and terrestrial measurements.

Sutherland, P, Melville WK.  2015.  Measuring turbulent kinetic energy dissipation at a wavy sea surface. Journal of Atmospheric and Oceanic Technology. 32:1498-1514.   10.1175/jtech-d-14-00227.1   AbstractWebsite

Wave breaking is thought to be the dominant mechanism for energy loss by the surface wave field. Breaking results in energetic and highly turbulent velocity fields, concentrated within approximately one wave height of the surface. To make meaningful estimates of wave energy dissipation in the upper ocean, it is then necessary to make accurate measurements of turbulent kinetic energy (TKE) dissipation very near the surface. However, the surface wave field makes measurements of turbulence at the air-sea interface challenging since the energy spectrum contains energy from both waves and turbulence over the same range of wavenumbers and frequencies. Furthermore, wave orbital velocities can advect the turbulent wake of instrumentation into the sampling volume of the instrument. In this work a new technique for measuring TKE dissipation at the sea surface that overcomes these difficulties is presented. Using a stereo pair of longwave infrared cameras, it is possible to reconstruct the surface displacement and velocity fields. The vorticity of that velocity field can then be considered to be representative of the rotational turbulence and not the irrotational wave orbital velocities. The turbulent kinetic energy dissipation rate can then be calculated by comparing the vorticity spectrum to a universal spectrum. Average surface TKE dissipation calculated in this manner was found to be consistent with near-surface values from the literature, and time-dependent dissipation was found to depend on breaking.

Deike, L, Popinet S, Melville WK.  2015.  Capillary effects on wave breaking. Journal of Fluid Mechanics. 769:541-569.   10.1017/jfm.2015.103   AbstractWebsite

We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier-Stokes equations for a two-phase air-water flow. A parametric study in terms of the Bond number, Bo, and the initial wave steepness, E, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of (is an element of, Bo) is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness cc defines the onset of wave breaking At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity-capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as is an element of similar to (1 + Bo)(-1/3). Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter b is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

Sutherland, P, Melville WK.  2015.  Field measurements of surface and near-surface turbulence in the presence of breaking waves. Journal of Physical Oceanography. 45:943-965.   10.1175/jpo-d-14-0133.1   AbstractWebsite

Wave breaking removes energy from the surface wave field and injects it into the upper ocean, where it is dissipated by viscosity. This paper presents an investigation of turbulent kinetic energy (TKE) dissipation beneath breaking waves. Wind, wave, and turbulence data were collected in the North Pacific Ocean aboard R/P FLIP, during the ONR-sponsored High Resolution Air-Sea Interaction (HiRes) and Radiance in a Dynamic Ocean (RaDyO) experiments. A new method for measuring TKE dissipation at the sea surface was combined with subsurface measurements to allow estimation of TKE dissipation over the entire wave-affected surface layer. Near the surface, dissipation decayed with depth as z(-1), and below approximately one significant wave height, it decayed more quickly, approaching z(-2). High levels of TKE dissipation very near the sea surface were consistent with the large fraction of wave energy dissipation attributed to non-air-entraining microbreakers. Comparison of measured profiles with large-eddy simulation results in the literature suggests that dissipation is concentrated closer to the surface than previously expected, largely because the simulations did not resolve microbreaking. Total integrated dissipation in the water column agreed well with dissipation by breaking for young waves, c(m)/u(*) <50 (where c(m) is the mean wave frequency and u(*) is the atmospheric friction velocity), implying that breaking was the dominant source of turbulence in those conditions. The results of these extensive measurements of near-surface dissipation over three field experiments are discussed in the context of observations and ocean boundary layer modeling efforts by other groups.

Melville, WK, Fedorov AV.  2015.  The equilibrium dynamics and statistics of gravity-capillary waves. Journal of Fluid Mechanics. 767:449-466.   10.1017/jfm.2014.740   AbstractWebsite

Recent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity W'aves of O(10) cm wavelength. 'fheories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity Waves. Thus the parasitic capillaries may provide the required dissipation of the short wind -generated gravity Waves. This has been the subject of speculation and conjecture in the literature, Using the nonlinear theory of Fedorov cV. Melville Fluid Mech., vol. 354, 1998, pp. 1-42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. 'The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (j. Mar Res., vol. 13, 1954, pp. 198-227) found contributed significantly to the mean square slope of the ocean surface, which they measured to be proportional to the wind speed. Here we show that the mean square slope predicted by the theory is proportional to the square of the friction velocity of the wind, IC, for small wave slopes, and approximately 14, for larger slopes.

Lenain, L, Melville WK.  2014.  Autonomous surface vehicle measurements of the ocean's response to Tropical Cyclone Freda. Journal of Atmospheric and Oceanic Technology. 31:2169-2190.   10.1175/jtech-d-14-00012.1   AbstractWebsite

On 31 December 2012, an instrumented autonomous surface vehicle (ASV; Wave Glider) transiting across the Pacific from Hawaii to Australia as part of the Pacific Crossing (PacX) project came very close (46 km) to the center of a category 3 Tropical Cyclone (TC), Freda, experiencing winds of up to 37 ms(-1) and significant wave heights close to 10 m. The Wave Glider was instrumented for surface ocean-lower atmosphere (SOLA) measurements, including atmospheric pressure, surface winds and temperature, sea surface temperature, salinity, dissolved oxygen, fluorescence (chlorophyll-a and turbidity), and surface-wave directional spectra. Such measurements in close proximity to a tropical cyclone are rare. This study presents novel observations of the ocean's response in three quadrants of TC Freda, collected from the instrumented glider. Evolution of the wind, the directional wave field, the sea surface temperature, and the Stokes drift profile (calculated from the wave directional spectrum) as Freda passed near the vehicle are examined. Results are discussed in the context of the recent coupled wind-wave modeling and large eddy simulation (LES) modeling of the marine boundary layer in Hurricane Frances (Sullivan et al. 2012). Processes by which cold nutrient-rich waters are entrained and mixed from below into the mixed layer as the TC passes near the Wave Glider are presented and discussed. The results of this encounter of an autonomous surface vehicle with TC Freda supports the use of ASVs for regular TC (hurricane) monitoring to complement remote sensing and "hurricane hunter" aircraft missions.

Sutherland, P, Melville WK.  2013.  Field measurements and scaling of ocean surface wave-breaking statistics. Geophysical Research Letters. 40:3074-3079.   10.1002/grl.50584   AbstractWebsite

[1] Deep-water breaking waves provide a mechanism for mass, momentum, and energy transfer between the atmosphere and ocean. Microscale breaking is particularly important, but notoriously difficult to measure in the field. In this paper, measurements from a new technique, using a stereo pair of long-wave infrared cameras to reconstruct the sea surface shape and velocity field, are presented. Breakers are detected using an image texture-based algorithm and then tracked on the reconstructed surface. These waves range from large air-entraining breakers to microbreakers that are undetectable by traditional visible video-based techniques. This allows measurements of breaker length distributions, (c), that extend to velocities near the gravity-capillary transition. These distributions are compared with measurements from the literature and from visible video imagery. A nondimensional scaling is proposed which collapses (c). Finally, estimates of energy dissipation and stress based on (c) are found to agree well with wave energy dissipation and wind stress models.

Pizzo, NE, Melville WK.  2013.  Vortex generation by deep-water breaking waves. Journal of Fluid Mechanics. 734:198-218.   10.1017/jfm.2013.453   AbstractWebsite

The connection between wave dissipation by breaking deep-water surface gravity waves and the resulting turbulence and mixing is crucial for an improved understanding of air-sea interaction processes. Starting with the ensemble-averaged Euler equations, governing the evolution of the mean flow, we model the forcing, associated with the breaking-induced Reynolds shear stresses, as a body force describing the bulk scale effects of a breaking deep-water surface gravity wave on the water column. From this, we derive an equation describing the generation of circulation, Gamma of the ensemble-average velocity field, due to the body force. By examining the relationship between a breaking wave and an impulsively forced fluid, we propose a functional form for the body force, allowing us to build upon the classical work on vortex ring phenomena to both quantify the circulation generated by a breaking wave and describe the vortex structure of the induced motion. Using scaling arguments, we show that Gamma = alpha(hk)(3/2)c(3)/g, where (c, h, k) represent a characteristic speed, height and wavenumber of the breaking wave, respectively, g is the acceleration due to gravity and alpha is a constant. This then allows us to find a direct relationship between the circulation and the wave energy dissipation rate per unit crest length due to breaking, epsilon(l). Finally, we compare our model and the available experimental data.

Grare, L, Lenain L, Melville WK.  2013.  Wave-coherent airflow and critical layers over ocean waves. Journal of Physical Oceanography. 43:2156-2172. AbstractWebsite

An analysis of coherent measurements of winds and waves from data collected during the Office of Naval Research (ONR) High-Resolution air-sea interaction (HiRes) program, from the Floating Instrument Platform (R/P FLIP), off the coast of northern California in June 2010 is presented. A suite of wind and wave measuring systems was deployed to resolve the modulation of the marine atmospheric boundary layer by waves. Spectral analysis of the data provided the wave-induced components of the wind velocity for various wind-wave conditions. The power spectral density, the amplitude, and the phase (relative to the waves) of these wave-induced components are computed and bin averaged over spectral wave age c/U(z) or c/u(*), where c is the linear phase speed of the waves, U(z) is the mean wind speed measured at the height z of the anemometer, and u(*) is the friction velocity in the air. Results are qualitatively consistent with the critical layer theory of Miles. Across the critical height z(c), defined such that U(z(c)) = c, the wave-induced vertical and horizontal velocities change significantly in both amplitude and phase. The measured wave-induced momentum flux shows that, for growing waves, less than 10% of the momentum flux at z approximate to 10 m is supported by waves longer than approximately 15 m. For older sea states, these waves are able to generate upward wave-induced momentum flux opposed to the overall downward momentum flux. The measured amplitude of this upward wave-induced momentum flux was up to 20% of the value of the total wind stress when C-p/u(*) > 60, where C-p is the phase speed at the peak of the wave spectrum.

Reineman, BD, Lenain L, Statom NM, Melville WK.  2013.  Development and testing of instrumentation for UAV-based flux measurements within terrestrial and marine atmospheric boundary layers. Journal of Atmospheric and Oceanic Technology. 30:1295-1319.   10.1175/jtech-d-12-00176.1   AbstractWebsite

Instrumentation packages have been developed for small (18-28 kg) unmanned aerial vehicles (UAVs) to measure momentum fluxes as well as latent, sensible, and radiative heat fluxes in the atmospheric boundary layer (ABL) and the topography below. Fast-response turbulence, hygrometer, and temperature probes permit turbulent momentum and heat flux measurements, and shortwave and longwave radiometers allow the determination of net radiation, surface temperature, and albedo. UAVs flying in vertical formation allow the direct measurement of fluxes within the ABL and, with onboard high-resolution visible and infrared video and laser altimetry, simultaneous observation of surface topography or ocean surface waves. The low altitude required for accurate flux measurements (typically assumed to be 30 m) is below the typical safety limit of manned research aircraft; however, with advances in laser altimeters, small-aircraft flight control, and real-time kinematic differential GPS, low-altitude flight is now within the capability of small UAV platforms. Flight tests of instrumented BAE Systems Manta C1 UAVs over land were conducted in January 2011 at McMillan Airfield (Camp Roberts, California). Flight tests of similarly instrumented Boeing Insitu ScanEagle UAVs were conducted in April 2012 at the Naval Surface Warfare Center, Dahlgren Division (Dahlgren, Virginia), where the first known measurements of water vapor, heat, and momentum fluxes were made from low-altitude (down to 30 m) UAV flights over water (Potomac River). This study presents a description of the instrumentation, summarizes results from flight tests, and discusses potential applications of these UAVs for (marine) atmospheric boundary layer studies.

Sullivan, PP, Romero L, McWilliams JC, Melville WK.  2012.  Transient Evolution of Langmuir Turbulence in Ocean Boundary Layers Driven by Hurricane Winds and Waves. Journal of Physical Oceanography. 42:1959-1980.   10.1175/jpo-d-12-025.1   AbstractWebsite

A large-eddy simulation (LES) model, which adopts wave-averaged equations with vortex force, is used to investigate Langmuir turbulence and ocean boundary layer (OBL) dynamics in high-wind hurricane conditions. The temporally evolving spatially asymmetric wind and wave Stokes drift velocity imposed in the LES are generated by a spectral wave prediction model adapted to Hurricane Frances traveling at a speed of 5.5 m s(-1). The potency of Langmuir turbulence depends on the turbulent Langmuir number, the wind-Stokes drift alignment, and the depth scale of the Stokes profile D-s relative to the OBL depth h. At the time of maximum winds, large-scale vigorous coherent cells develop on the right-hand side of the storm under the inertially rotating winds; the Stokes drift velocity is well tuned to the surface winds. Much weaker cells develop on the left-hand side of the storm, partly because of reduced Stokes production. With misaligned winds and waves the vertical momentum fluxes can be counter to the gradient of Stokes drift, and the cell orientation tracks the direction of the mean Lagrangian shear. The entrainment flux is increased by 20% and the sea surface temperature is 0.25 K cooler on the right-hand side of the storm in the presence of Langmuir turbulence. Wave effects impact entrainment when the ratio D-s/vertical bar h vertical bar > 0.75. Because of wind-wave asymmetry Langmuir cells add quantitatively to the left-right asymmetry already understood for hurricanes due to resonance. And the transient evolution of the OBL cannot be understood simply in terms of equilibrium snapshots.

Huang, ZC, Reineman BD, Lenain L, Melville WK, Middleton JH.  2012.  Airborne lidar measurements of wave energy dissipation in a coral reef lagoon system. Journal of Geophysical Research-Oceans. 117   10.1029/2011jc007203   AbstractWebsite

Quantification of the turbulent kinetic energy dissipation rate in the water column, epsilon, is very important for assessing nutrient uptake rates of corals and therefore the health of coral reef lagoon systems. However, the availability of such data is limited. Recently, at Lady Elliot Island (LEI), Australia, we showed that there was a strong correlation between in situ measurements of surface-wave energy dissipation and epsilon. Previously, Reineman et al. (2009), we showed that a small airborne scanning lidar system could measure the surface wavefield remotely. Here we present measurements demonstrating the use of the same airborne lidar to remotely measure surface wave energy fluxes and dissipation and thereby estimate epsilon in the LEI reef-lagoon system. The wave energy flux and wave dissipation rate across the fore reef and into the lagoon are determined from the airborne measurements of the wavefield. Using these techniques, observed spatial profiles of energy flux and wave energy dissipation rates over the LEI reef-lagoon system are presented. The results show that the high lidar backscatter intensity and point density coming from the high reflectivity of the foam from depth-limited breaking waves coincides with the high wave-energy dissipation rates. Good correlations between the airborne measurements and in situ observations demonstrate that it is feasible to apply airborne lidar systems for large-scale, long-term studies in monitoring important physical processes in coral reef environments. When added to other airborne techniques, the opportunities for efficient monitoring of large reef systems may be expanded significantly.

Huang, ZC, Lenain L, Melville WK, Middleton JH, Reineman B, Statom N, McCabe RM.  2012.  Dissipation of wave energy and turbulence in a shallow coral reef lagoon. Journal of Geophysical Research-Oceans. 117   10.1029/2011jc007202   AbstractWebsite

Simultaneous in situ measurements of waves, currents and turbulence are presented to describe dissipation rates of wave energy and turbulent kinetic energy in the windward coral reef-lagoon system at Lady Elliot Island (LEI), Australia. The dissipation of wave energy in the lagoon is tidally modulated and strongly correlates with frictional dissipation due to the presence of the extremely rough bottom boundary. The observed turbulent kinetic energy (TKE) dissipation rate, epsilon, in this wave-dominated lagoon is much larger than recently reported values for unidirectional flows over natural fringing coral reefs. The correlation between the wave dissipation and. is examined. The average rate of dissipation induced by the rough turbulent flow was estimated directly from the observed. coupled with both a depth-integrated approach and with a bottom boundary layer scaling. Rates of TKE dissipation estimated using the two approaches approximate well, within a factor of 1.5 to 2.4, to the surface-wave energy dissipation rate. The wave dissipation and friction factor in the lagoon can be described by a spectral wave-frictional model with a bottom roughness length scale that is approximately constant across the lagoon. We also present estimates of dissipation induced by the canopy drag force of the coral heads. The dissipation in this case is enhanced and becomes more significant for the total energy dissipation when the water depth in the lagoon is comparable to the height of the coral heads.

Dickey, T, Banner ML, Bhandari P, Boyd T, Carvalho L, Chang G, Chao Y, Czerski H, Darecki M, Dong C, Farmer D, Freeman S, Gemmrich J, Gernez P, Hall-Patch N, Holt B, Jiang S, Jones C, Kattawar G, LeBel D, Lenain L, Lewis M, Liu Y, Logan L, Manov D, Melville WK, Moline MA, Morison R, Nencioli F, Pegau WS, Reineman B, Robbins I, Rottgers R, Schultz H, Shen L, Shinki M, Slivkoff M, Sokolski M, Spada F, Statom N, Stramski D, Sutherland P, Twardowski M, Vagle S, Van Dommelen R, Voss K, Washburn L, Wei J, Wijesekera H, Wurl O, Yang D, Yildiz S, You Y, Yue DKP, Zaneveld R, Zappa CJ.  2012.  Introduction to special section on Recent Advances in the Study of Optical Variability in the Near-Surface and Upper Ocean. Journal of Geophysical Research-Oceans. 117   10.1029/2012jc007964   AbstractWebsite

Optical variability occurs in the near-surface and upper ocean on very short time and space scales (e.g., milliseconds and millimeters and less) as well as greater scales. This variability is caused by solar, meteorological, and other physical forcing as well as biological and chemical processes that affect optical properties and their distributions, which in turn control the propagation of light across the air-sea interface and within the upper ocean. Recent developments in several technologies and modeling capabilities have enabled the investigation of a variety of fundamental and applied problems related to upper ocean physics, chemistry, and light propagation and utilization in the dynamic near-surface ocean. The purpose here is to provide background for and an introduction to a collection of papers devoted to new technologies and observational results as well as model simulations, which are facilitating new insights into optical variability and light propagation in the ocean as they are affected by changing atmospheric and oceanic conditions.

Romero, L, Melville WK.  2011.  Spatial Statistics of the Sea Surface in Fetch-Limited Conditions. Journal of Physical Oceanography. 41:1821-1841.   10.1175/2011jpo4535.1   AbstractWebsite

An analysis of airborne wave observations collected in the Gulf of Tehuantepec is presented. The data include lidar measurements of the surface displacement as a function of two horizontal dimensions in fetch-limited conditions, with fetches between 20 and 500 km and winds between 10 and 20 m s(-1). The spatial data have an advantage over the commonly used single-point time series measurements, allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding various thresholds. This study presents an analysis of several statistical wind wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths; the pdf of wave heights, wavenumber vectors, and wave slopes; as well as the statistics of the lengths of crests exceeding threshold wave heights and slopes. The empirical findings from the lidar data are compared against analytical theories in the literature, including some that had not been tested previously with field data such as the work by M. S. Longuet-Higgins describing the length of contours surrounding large wave heights per unit surface area. The effect of second-order nonlinearities on the distribution of crest lengths per unit surface area is investigated with analytical approximations and stochastic numerical simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest-length distribution of large waves by a factor of 2 or more.