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Lenain, L, Pizzo N, Melville WK.  2019.  Laboratory studies of Lagrangian transport by breaking surface waves. Journal of Fluid Mechanics. 876   10.1017/jfm.2019.544   AbstractWebsite

While it has long been recognized that Lagrangian drift at the ocean surface plays a critical role in the kinematics and dynamics of upper ocean processes, only recently has the contribution of wave breaking to this drift begun to be investigated through direct numerical simulations (Deike et al., J. Fluid Mech., vol. 829, 2017, pp. 364-391; Pizzo et al., J. Phys. Oceanogr., vol. 49(4), 2019, pp. 983-992). In this work, laboratory measurements of the surface Lagrangian transport due to focusing deep-water non-breaking and breaking waves are presented. It is found that wave breaking greatly enhances mass transport, compared to non-breaking focusing wave packets. These results are in agreement with the direct numerical simulations of Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364-391), and the increased transport due to breaking agrees with their scaling argument. In particular, the transport at the surface scales with , the linear prediction of the maximum slope at focusing, while the surface transport due to non-breaking waves scales with, in agreement with the classical Stokes prediction.

Pizzo, N, Melville WK.  2019.  Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model. Journal of Fluid Mechanics. 873:238-259.   10.1017/jfm.2019.428   AbstractWebsite

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrodinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105-114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$ , for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air-sea interaction processes is discussed.

Pizzo, N, Melville WK, Deike L.  2019.  Lagrangian transport by nonbreaking and breaking deep-water waves at the ocean surface. Journal of Physical Oceanography. 49:983-992.   10.1175/jpo-d-18-0227.1   AbstractWebsite

Using direct numerical simulations (DNS), Deike et al. found that the wave-breaking-induced mass transport, or drift, at the surface for a single breaking wave scales linearly with the slope of a focusing wave packet, and may be up to an order of magnitude larger than the prediction of the classical Stokes drift. This model for the drift due to an individual breaking wave, together with the statistics of wave breaking measured in the field, are used to compute the Lagrangian drift of breaking waves in the ocean. It is found that breaking may contribute up to an additional 30% to the predicted values of the classical Stokes drift of the wave field for the field experiments considered here, which have wind speeds ranging from 1.6 to 16 m s(-1), significant wave heights in the range of 0.7-4.7 m, and wave ages (defined here as c(m)/u(*), for the spectrally weighted phase velocity c(m) and the wind friction velocity u(*)) ranging from 16 to 150. The drift induced by wave breaking becomes increasingly more important with increasing wind friction velocity and increasing significant wave height.

Grare, L, Lenain L, Melville WK.  2018.  Vertical profiles of the wave-induced airflow above ocean surface waves. Journal of Physical Oceanography. 48:2901-2922.   10.1175/jpo-d-18-0121.1   AbstractWebsite

An analysis of coherent measurements of winds and waves from data collected during the ONR Southern California 2013 (SoCal2013) program from R/P FLIP off the coast of Southern California in November 2013 is presented. An array of ultrasonic anemometers mounted on a telescopic mast was deployed to resolve the vertical profile of the modulation of the marine atmospheric boundary layer by the waves. Spectral analysis of the data provides the wave-induced components of the wind velocity for various wind-wave conditions. Results show that the wave-induced fluctuations depend both on the spectral wave age c(omega)/U(z) and the normalized height kz, where c is the linear phase speed of the waves with wavenumber k and U(z) is the mean wind speed measured at the height z. The dependence on the spectral wave age expresses the sensitivity of the wave-induced airflow to the critical layer where U(z) = c. Across the critical layer, there is a significant change of both the amplitude and phase of the wave-induced fluctuations. Below the critical layer, the phase remains constant while the amplitude decays exponentially depending on the normalized height. Accounting for this double dependency, the nondimensionalization of the amplitude of the wave-induced fluctuations by the surface orbital velocity akc collapses all the data measured by the array of sonic anemometers, where a is the amplitude of the waves.

Young, AP, Flick RE, Gallien TW, Giddings SN, Guza RT, Harvey M, Lenain L, Ludka BC, Melville KW, O'Reilly WC.  2018.  Southern California coastal response to the 2015–2016 El Niño. Journal of Geophysical Research: Earth Surface. 123:3069-3083.   10.1029/2018JF004771   AbstractWebsite

Widespread erosion associated with energetic waves of the strong 2015–2016 El Niño 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 2015–2016, in Southern California, total water levels (sum of tides, anomalies, and wave superelevation) were lower than during the 1997–1998 Niño, and comparable to the 2009–2010 Niño. 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 2009–2010 El Niño. Some San Diego county beaches were narrower in the 1997–1998 El Niño than in 2015–2016, consistent with the higher erosion potential in 1997–1998. 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 1997–1998 El Niño, because of low rainfall, a northerly swell approach, and relatively limited total high-water levels.

Deike, L, Melville WK.  2018.  Gas transfer by breaking waves. Geophysical Research Letters. 45:10482-10492.   10.1029/2018gl078758   AbstractWebsite

The transfer of gases at the ocean-atmosphere interface impacts weather and climate from local to global scales, with carbon dioxide (CO2) key to marine life and ecosystems, and dimethyl sulfide affecting aerosols and atmospheric processes. However, the bubble-mediated gas transfer, associated with breaking waves has remained poorly constrained. We present a spectral framework for bubble-mediated gas transfer, computed from a mechanistic model for air bubble entrainment at the breaking wave scale combined with a chemical model. Gas transfer is upscaled to the ocean scale by evaluating air entrainment at all wave scales using wave and wave breaking statistics. The obtained CO2 gas transfer velocity reproduces the variability of historical parameterizations and recent field measurements, with very good accuracy. We propose a wind-wave parameterization that collapses all available data, which can be directly implemented in ocean-wave models or used with remote sensing of the ocean surface to infer gas transfer. Plain Language Summary The transfer of gases at the ocean-atmosphere interface impacts weather and climate from local to global scales. The exchanges of carbon dioxide and oxygen are key to marine life and ecosystems, while transfer of dimethyl sulfide has a strong effect on aerosol composition, affecting atmospheric processes. Yet the bubble-mediated gas transfer, associated with breaking waves has remained poorly constrained. We present a general framework for gas transfer in the open ocean, where air entrainment and the associated bubble-mediated gas transfer are evaluated at all scales. We combine a mechanistic model for air entrainment and bubble statistics at the breaking wave scale with a chemical model for gas transfer by the entrained air bubbles and then upscale the gas exchange using the wave and wave breaking statistics. The obtained gas transfer velocity for CO2 reproduces the variability of historical parameterizations and recent field measurements, with very good accuracy, and we propose a wind-wave parameterization that collapse all available data. The proposed model for gas transfer can be directly implemented in coupled ocean-wave models, or used with remote sensing data of the ocean surface to infer gas transfer, strongly improving predictions of gas exchange at the ocean-atmosphere interface.

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.