Wave dissipation by breaking, or the energy transfer from the surface wave field to currents and turbulence, is one of the least understood components of air-sea interaction. It is important for a better understanding of the Coupling between the surface wave field and the upper layers of the ocean and for improved surface-wave prediction schemes. Simple scaling arguments show that the wave dissipation per 5 unit length of breaking crest, cl, should be proportional to rho(w)gc(5), where rho(w) is the density of water, g is the acceleration due to gravity and c is the phase speed of the breaking wave. The proportionality factor, or 'breaking parameter' b, has been poorly constrained by experiments and field measurements, although our earlier work has Suggested that it should be dependent oil measures of the wave slope and spectral bandwidth. In this paper we describe inertial scaling arguments for the energy lost by plunging breakers which predict that the breaking parameter b=beta(hk)(5/2), where hk is a local breaking slope parameter, and P is a parameter of 0(1). This prediction is tested with laboratory measurements of breaking Clue to dispersive focusing of wave packets in a wave channel. Good agreement is Found within the scatter of the data. We also find that if an integral linear measure of the maximum Slope Of the wave packet, S, is used instead of hk, then b proportional to S-2.77 gives better agreement with the data. During the final preparation of this paper we became aware of similar experiments by Banner & Peirson (2007) concentrating oil the threshold for breaking at lower wave slopes, using a measure of the rate of focusing of wave energy to correlate measurements of b. We discuss the significance of these results in the context of recent measurements and modelling of surface wave processes.

Air-sea fluxes of heat and momentum play a crucial role in weather, climate, and the coupled general circulation of the oceans and atmosphere. Much progress has been made to quantify momentum transfer from the atmosphere to the ocean for a wide range of wind and wave conditions. Yet, despite the fact that global heat budgets are now at the forefront of current research in atmospheric, oceanographic, and climate problems and despite the good research progress in recent years, much remains to be done to better understand and quantify air-sea heat transfer. It is well known that ocean-surface waves may support momentum transfer from the atmosphere to the ocean, but the role of the waves in heat transfer has been ambiguous and poorly understood. Here, evidence is presented that there are surface wave-coherent components of both the sensible and the latent heat fluxes. Presented here are data from three field experiments that show modulations of temperature and humidity at the surface and at 10-14 m above the surface, which are coherent with the surface wave field. The authors show that the phase relationship between temperature and surface displacement is a function of wind speed. At a 10-12-m elevation, a wave-coherent heat transfer of O( 1) W m(-2) is found, dominated by the latent heat transfer, as well as wave-coherent fractional contributions to the total heat flux ( the sum of latent and sensible heat fluxes) of up to 7%. For the wind speeds and wave conditions of these experiments, which encompass the range of global averages, this wave contribution to total heat flux is comparable in magnitude to the atmospheric heat fluxes commonly attributed to the effects of greenhouse gases or aerosols. By analogy with momentum transfer, the authors expect the wave-coherent heat transfer to decay with height over scales on the order of k(-1), where k is the characteristic surface wavenumber; therefore, it is also expected that measurements at elevations of O( 10) m may underestimate the contribution of the wave-induced heat flux to the atmosphere.

Ocean surface processes, and air-sea interaction in general, have recently received increased attention because it is now accepted that small-scale surface phenomena can play a crucial role in the air-sea fluxes of heat, mass, and momentum, with important implications for weather and climate studies. Yet, despite good progress in recent years, the air-sea interface and the adjacent atmospheric and marine boundary layers have proven to be difficult to measure in all but the most benign conditions. This has led to the need for novel measurement techniques to quantify processes of air-sea interaction. Here the authors present infrared techniques aimed at simultaneously studying multiple aspects of the air-sea interface and air-sea fluxes. The instrumentation was tested and deployed during several field experiments from Research Platform (R/P) FLIP and Scripps pier. It is shown that these techniques permit the detailed study of the ocean surface temperature and velocity fields. In particular, it is shown that cross-correlation techniques typically used in particle image velocimetry can be used to infer the ocean surface velocity field from passive infrared temperature images. In addition, when conditions make cross-correlation techniques less effective, an active infrared marking and tracking technique [which will be called thermal marker velocimetry (TMV)] can be successfully used to measure the surface velocity and its spatial and temporal derivatives. The thermal marker velocimetry technique also provides estimates of the heat transfer velocity and surface renewal frequencies. Finally, infrared altimetry is used to complement the temperature and kinematic data obtained from passive imagery and active marking. The data obtained during the testing and deployment of this instrumentation provide a novel description of the kinematics of the surface of the ocean.

The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.

A field experiment to study the spectral balance of the source terms for wind-generated waves in finite water depth was carried out in Lake George, Australia. The measurements were made from a shore-connected platform at varying water depths from 1.2 m down to 20 cm. Wind conditions and the geometry of the lake were such that fetch-limited conditions with fetches ranging from approximately 10 km down to 1 km prevailed. The resulting waves were intermediate-depth wind waves with inverse wave ages in the range 1 < U-10/C-p < 8. The atmospheric input, bottom friction, and whitecap dissipation were measured directly and synchronously by an integrated measurement system, described in the paper. In addition, simultaneous data defining the directional wave spectrum, atmospheric boundary layer profile, and atmospheric turbulence were available. The contribution to the spectral evolution due to nonlinear interactions of various orders is investigated by a combination of bispectral analysis of the data and numerical modeling. The relatively small scale of the lake enabled experimental conditions such as the wind field and bathymetry to be well defined. The observations were conducted over a 3-yr period, from September 1997 to August 2000, with a designated intensive measurement period [the Australian Shallow Water Experiment (AUSWEX)] carried out in August-September 1999. High data return was achieved.

Using three-dimensional Monte Carlo radiative transfer simulations, we examine the effect of beam transmissometer geometry on the relative error in the measurement of the beam-attenuation coefficient in an aquatic environment characterized by intense light scattering, especially within submerged bubble clouds entrained by surface-wave breaking. We discuss the forward-scattering error associated with the detection of photons scattered at small angles (<1degrees) and the multiple-scattering error associated with the detection of photons scattered more than once along the path length of the instrument. Several scattering phase functions describing bubble clouds at different bubble void fractions in the water are considered. Owing to forward-scattering error, a beam-attenuation meter (beam transmissometer) with a half-angle of receiver acceptance of 1.0degrees and a path length of 0.1 m can underestimate the true beam attenuation within the bubble cloud by more than 50%. For bubble clouds with a beam attenuation of as much as 100 m(-1), the multiple-scattering error is no more than a few percent. These results are compared with simulations for some example phase functions that are representative of other scattering regimes found in natural waters. The forward-scattering error for the Petzold phase function of turbid waters is 16% for a typical instrument geometry, whereas for the Henyey-Greenstein phase function with the asymmetry parameter of 0.7 and 0.9 the error range is 8-28%. (C) 2004 Optical Society of America.

We present measurements of Ku band electromagnetic ( EM) bias made for 2 months from a platform in Bass Strait off the southeast coast of Australia during the austral winter of 1992. EM bias, epsilon, the difference between the electromagnetic and true mean sea levels, was measured using Doppler scatterometers. Linear wave theory was used to relate the Doppler signal to the surface displacement, giving simultaneous coincident backscatter and wave measurements, including significant wave height, H-s. On the basis of dimensional reasoning, we suggest that the usual inhomogeneous correlations of the normalized bias beta = epsilon/H-s with the 10 m wind speed, U-10, and H-s may be improved by correlating the data with nondimensional variables, including a characteristic wave slope, s, and wave age, c/U-10, where c is a characteristic phase speed of the surface waves. Using both polynomial correlations and optimal estimation techniques to fit the data, we find that the standard error of the fit is reduced by similar to50% when the dimensionless variables are used. We find that the dependence of the EM bias on the wave slope is consistent with earlier tower-based measurements and the theory of short-wave modulation by longer waves. We discuss the implications of these results for operational implementation of EM bias algorithms based on wave slope and wave age.

We devise a stochastic model for the effects of breaking waves and fit its distribution functions to laboratory and field data. This is used to represent the space-time structure of momentum and energy forcing of the oceanic boundary layer in turbulence-resolving simulations. The aptness of this breaker model is evaluated in a direct numerical simulation (DNS) of an otherwise quiescent fluid driven by an isolated breaking wave, and the results are in good agreement with laboratory measurements. The breaker model faithfully reproduces the bulk features of a breaking event: the mean kinetic energy decays at a rate approaching t(-1), and a long-lived vortex (eddy) is generated close to the water surface. The long lifetime of this vortex (more than 50 wave periods) makes it effective in energizing the surface region of oceanic boundary layers. Next., a comparison of several different DNS of idealized oceanic boundary layers driven by different surface forcing (i.e. constant current (as in Couette flow), constant stress, or a mixture of constant stress plus stochastic breakers) elucidates the importance of intermittent stress transmission to the underlying currents. A small amount of active breaking, about 1.6% of the total water surface area at any instant in time, significantly alters the instantaneous flow patterns as well as the ensemble statistics. Near the water surface a vigorous downwelling-upwelling pattern develops at the head and tail of each three-dimensional breaker. This enhances the vertical velocity variance and generates both negative- and positive-signed vertical momentum flux. Analysis of the mean velocity and scalar profiles shows that breaking effectively increases the surface roughness z(0) by more than a factor of 30; for our simulations z(0)/lambda approximate to 0.04 to 0.06, where lambda is the wavelength of the breaking wave. Compared to a flow driven by a constant current, the extra mixing from breakers increases the mean eddy viscosity by more than a factor of 10 near the water surface. Breaking waves alter the usual balance of production and dissipation in the turbulent kinetic energy (TKE) budget; turbulent and pressure transports and breaker work are important sources and sinks in the budget. We also show that turbulent boundary layers driven by constant current and constant stress (i.e. with no breaking) differ in fundamental ways. The additional freedom provided by a constant-stress boundary condition permits finite velocity variances at the water surface, so that flows driven by constant stress mimic flows with weakly and statistically homogeneous breaking waves.

[1] For quantitative studies of the ocean using altimetric measurements, the sea surface height measurements must be corrected for the electromagnetic ( EM) bias effect. Project-provided EM bias correction algorithms were derived from the altimeter data as a function of wind speed and wave height through variance minimization techniques [ Gaspar et al., 1994]. In this paper we characterize the impact of those corrections on the altimeter data and compare it with an empirical algorithm based on tower observations of wave slopes and wave age ( W. K. Melville et al., Wave slope and wave age effects in measurements of EM bias, submitted to Journal of Geophysical Research, 2002) and with theoretical predictions of EM bias [ Srokosz, 1986]. We find a significant correlation between high- frequency ocean signals with the project- provided EM bias correction. This suggests that an EM bias algorithm cannot be estimated from altimeter data alone through variance minimization techniques. Since the EM bias depends on parameters that cannot be measured by an altimeter ( e. g., wave slope), improved theoretical corrections appear to be preferable to altimetry- based empirical estimates. Using wave buoy and wave model ( WAM) data, we find good agreement between existing theoretical correction and empirical corrections based on wave slope and wave age information over a significant range of parameters. Although further work is needed to extend our tests of algorithms to larger wave slopes, existing wave slope and wave age- based algorithms appear comparable in goodness to project- provided empirical algorithms and may be used for routine altimetry processing in combination with WAM output on a global basis.

Surface waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean. The development of the wave field depends on wind, wave-wave and wave-current interactions and wave dissipation owing to breaking, which is accompanied by momentum fluxes from waves to currents. Wave breaking supports air-sea fluxes of heat and gas(1,2), which have a profound effect on weather and climate. But wave breaking is poorly quantified and understood. Here we present measurements of wave breaking, using aerial imaging and analysis, and provide a statistical description of related sea-surface processes. We find that the distribution of the length of breaking fronts per unit area of sea surface is proportional to the cube of the wind speed and that, within the measured range of the speed of the wave fronts, the length of breaking fronts per unit area is an exponential function of the speed of the front. We also find that the fraction of the ocean surface mixed by breaking waves, which is important for air-sea exchange, is dominated by wave breaking at low velocities and short wavelengths.

Digital particle image velocimetry (DPIV) measurements of the velocity field under breaking waves in the laboratory are presented. The region of turbulent fluid directly generated by breaking is too large to be imaged in one video frame and so an ensemble-averaged representation of the flow is built up from a mosaic of image frames. It is found that breaking generates at least one coherent vortex that slowly propagates downstream at a speed consistent with the velocity induced by its image in the free surface. Both the kinetic energy of the flow and the vorticity decay approximately as t(-1). The Reynolds stress of the turbulence also decays as t(-1) and is, within the accuracy of the measurements, everywhere negative, consistent with downward transport of streamwise momentum. Estimates of the mometum flux from waves to currents based on the measurements of the Reynolds stress are consistent with earlier estimates. The implications of the measurements for breaking in the field are discussed. Based on geometrical optics and wave action conservation, we suggest that the presence of the breaking-induced vortex provides an explanation for the suppression of short waves by breaking. Finally, in Appendices, estimates of the majority of the terms in the turbulent kinetic energy budget are presented at an early stage in the evolution of the turbulence, and comparisons with independent acoustical measurements of breaking are presented.

We present the results of laboratory and field measurements on the stability of wind-driven water surfaces. The laboratory measurements show that when exposed to an increasing wind starting from rest, surface current and wave generation is accompanied by a variety of phenomena that occur over comparable space and time scales. Of particular interest is the generation of small-scale, streamwise vortices, or Langmuir circulations, the clear influence of the circulations on the structure of the growing wave field, and the subsequent transition to turbulence of the surface flow. Following recent work by Melville, Shear & Veron (1998) and Veron & Melville (1999b), we show that the waves that are initially generated by the wind are then strongly modulated by the Langmuir circulations that follow. Direct measurements of the modulated wave variables are qualitatively consistent with geometrical optics and wave action conservation, but quantitative, comparison remains elusive. Within the range of parameters of the experiments, both the surface waves and the Langmuir circulations first appear at constant Reynolds numbers of 370 +/- 10 and 530 +/- 20, respectively, based on the surface velocity and the depth of the laminar shear layer. The onset of the Langmuir circulations leads to a significant increase in the heat transfer across the surface. The field measurements in a boat basin display the same phenomena that are observed in the laboratory. The implications of the measurements for air-sea fluxes, especially heat and gas transfer, and sea-surface temperature, are discussed.

Breaking waves at the ocean's surface inject bubbles and turbulence into the water column. During periods of rough weather the scales of wave breaking will increase with increasing sea states and result in mixing of the surface waters and the turbulent transport of bubbles to depth. Depending on their concentrations and size distribution, the entrained bubbles can significantly change the optical properties of water, introducing potentially significant errors in retrieval of remotely sensed hyperspectral data products. In this paper, the effects of bubbles on optical scattering in the upper ocean are investigated through optical scattering calculations based on field measurements of bubble populations. The field measurements were obtained offshore Point Conception, California, in June 1997, using an acoustical technique which measured the bubble size distribution at 2 Hz from a surface buoy designed to follow the longer waves. The effects of the bubbles on the bulk optical scattering and backscattering coefficients, b and b(b), respectively, are determined by using the acoustically measured size distributions, and size-dependent scattering efficiencies based on Mie scattering calculations. Time series of the bubble distributions measured in rough conditions (wind speed, U-10 = 15 m/s, significant wave height, H-1/3 = 3.2 m) suggest that the bubble contribution to light scattering is highly variable near the ocean surface, with values divning roughly 5 decades over time periods of O(10) minutes. Bubble size distributions measured at a 0.7-m depth indicate that the optical effects of the bubbles on b(b), and hence the remote sensing reflectance, will be significant at bubble void fractions above 10(-6) and that the bubble contribution to total b(b) will exceed values of 10(-2) m(-1) inside bubble clouds.

Properties of internal wave fronts or Kelvin fronts travelling eastward in the equatorial waveguide are studied, motivated by recent studies on coastal Kelvin waves and jumps and new data on equatorial Kelvin waves. It has been recognized for some time that nonlinear equatorial Kelvin waves can steepen and break, forming a broken wave of depression, or front, propagating eastward. The three-dimensional structure of the wave field associated with such a front is considered. As for linear Kelvin waves, the front is symmetrical with respect to the equator. Sufficiently far away from the front, the wave profile is Gaussian in the meridional direction, with the equatorial Rossby radius of deformation being its decay scale. Due to nonlinearity, the phase speed of the front is greater than that of linear Kelvin waves, resulting in a supercritical Row. This leads to the resonant generation of equatorially trapped gravity-inertial (or Poincare) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincare waves are generated, with their wavelength determined by the amplitude of the front. Finally. the propagation of a Kelvin front gives rise to a nonzero poleward mass transport above the thermocline, in consequence of which there is a poleward heat flux.

The development of a broadband sound velocimeter that allows the simultaneous measurement of sound speed and attenuation over a wide range of frequencies is described. The velocimeter measures the attenuation and dispersion of a broadband acoustic pulse over frequencies ranging from 4 to 100 kHz across a fixed pathlength using a two-transducer system. The resulting data are inverted to arrive at bubble size distributions over bubble radii in the range 30-800 mu m. The instrument was tested in the large wave channel at the Hydraulics Laboratory of Scripps Institution of Oceanography. The channel can generate breaking waves of 0(1 m) height using a hydraulically driven wave generator, giving bubble size distributions similar to those found in the field. The presence of the bubbles significantly changes the acoustical properties of the water. internal consistency checks of the acoustic data and measurements of bubbles using an independent optical sizing technique support the accuracy of the acoustic system in measuring bubble size distributions. A field test of the system was performed off Scripps Pier in water of approximately 6-m depth. Observations demonstrate that bubble transport events with significant temporal and spatial variability are associated with rip currents and introduce significant vertical gradients in the acoustical properties of the water. The performance of the system in the field was found to be comparable to that found in the laboratory.

This paper presents laboratory and field testing of a pulse-to-purse coherent acoustic Doppler profiler for the measurement of turbulence in the ocean. In the laboratory, velocities and wavenumber spectra collected From Doppler and digital particle image velocimeter measurements compare very well. Turbulent velocities are obtained by identifying and filtering out deep water gravity waves in Fourier space and inverting the result. Spectra of the velocity profiles then reveal the presence of an inertial subrange in the turbulence generated by unsteady breaking waves. In the field, comparison of the profiler velocity records with a single-point current measurement is satisfactory. Again wavenumber spectra are directly measured and exhibit an approximate -5/3 slope. It is concluded that the instrument is capable of directly resolving the wavenumber spectral levels in the inertial subrange under breaking waves, and therefore is capable of measuring dissipation and other turbulence parameters in the upper mixed layer or surface-wave zone.

Laboratory measurements of the fine space-time structure of short gravity-capillary waves, as well as lice-band scattering at grazing and moderate incidence fr om wind waves in the large Delft Hydraulics Laboratory wind-wave channel are presented, This study was stimulated by the need to verify the processes that significantly contribute to scattering at grazing and moderate incidence, A scanning laser slope gauge was used for measuring capillary waves from 2-mm to 2-cm wavelengths and frequencies ranging up to 100 Hz, A dual-polarized (vertical, VV, and horizontal, HH), coherent, pulsed Ku-band scatterometer with good temporal resolution (3 ns) was used to obtain simultaneous Doppler spectra and the absolute cross section of scattered signals for grazing angles 6 and 25 degrees and for winds in the range 2.5-12.5 m/s, Two-dimensional (2-D) filtering and bispectral analyses were used to separate and study the influence of free and bound surface waves. The results of this study demonstrate that the frequency-wavenumber spectra of capillary waves consist of two parts, The first corresponds to free capillary waves, which satisfy the dispersion relationship, The second corresponds to bound parasitic capillary waves, which are located near the crests of steep wind waves. The phase velocity of these capillary waves is approximately equal to the phase velocity of the steep waves. Measurements of the Doppler frequency of the scattered signals show that the Doppler spectra also have a bimodal structure, While the first low-frequency part of the spectrum corresponds to the Bragg scattering from the free capillary waves, the high-frequency part is associated with Bragg scattering from the bound capillary waves on the crests of the steep waves. This type of scattering is predominant for the upwind direction of illumination (especially for HH-polarization).

We report laboratory measurements of nonlinear parasitic capillary waves generated by longer waves in a channel. The experiments are conducted for three frequencies of longer waves (4, 5, and 6 Hz), corresponding to wavelengths of approximately 11, 7, and 5 cm. For these wavelengths we apply a model developed recently by Fedorov and Melville [J. Fluid Mech. 354, 1 (1998)] to predict the wave profile. Based on a viscous boundary layer approximation near the surface, the model enables us to efficiently calculate gravity-capillary waves. We present direct comparisons that show good agreement between the measurements and numerical predictions over a range of parameters. Finally, we give some simple estimates for a sharp cutoff in the wave number spectra observed in both the numerical solutions and the laboratory measurements of shea gravity-capillary waves. (C) 1998 American Institute of Physics.

Some of the highlights of an experiment designed to study coastal atmospheric phenomena along the California coast (Coastal Waves 1996 experiment) are described. This study was designed to address several problems, including the cross-shore variability and turbulent structure of the marine boundary layer, the influence of the coast on the development of the marine layer and clouds, the ageostrophy of the flow, the dynamics of trapped events, the parameterization of surface fluxes, and the supercriticality of the marine layer. Based in Monterey, California, the National Center for Atmospheric Research (NCAR) C-130 Hercules and the University of North Carolina Piper Seneca obtained a comprehensive set of measurements on the structure of the marine layer. The study focused on the effects of prominent topographic features on the wind. Downstream of capes and points, narrow bands of high winds are frequently encountered. The NCAR-designed Scanning Aerosol Backscatter Lidar (SABL) provided a unique opportunity to connect changes in the depth of the boundary layer with specific features in the dynamics of the flow field. An integral part of the experiment was the use of numerical models as forecast and diagnostic tools. The Naval Research Laboratory's Coupled Ocean Atmosphere Model System (COAMPS) provided high-resolution forecasts of the wind field in the vicinity of capes and points, which aided the deployment of the aircraft. Subsequently, this model and the MIUU (University of Uppsala) numerical model were used to support the analysis of the field data. These are some of the most comprehensive measurements of the topographically forced marine layer that have been collected. SABL proved to be an exceptionally useful tool to resolve the small-scale structure of the boundary layer and, combined with in situ turbulence measurements, provides new insight into the structure of the marine atmosphere. Measurements were made sufficiently far offshore to distinguish between the coastal and open ocean effects. COAMPS proved to be an excellent forecast tool and both it and the MIUU model are integral parts of the ongoing analysis. The results highlight the large spatial variability that occurs directly in response to topographic effects. Routine measurements are insufficient to resolve this variability. Numerical weather prediction model boundary conditions cannot properly define the forecast system and often underestimate the wind speed and surface wave conditions in the nearshore region. This study was a collaborative effort between the National Science Foundation, the Office of Naval Research, the Naval Research Laboratory, and the National Oceanographic and Atmospheric Administration.

We present laboratory measurements of the generation and evolution of Langmuir circulations as an instability of a wind-driven surface shear layer. The shear layer, which is generated by an accelerating wind starting from rest above a quiescent water surface, both accelerates and deepens monotonically until the inception of the Langmuir circulations. The Langmuir circulations closely follow the initial growth of the wind waves and rapidly lead to vertical mixing of the horizontal momentum and a deceleration of the surface layer. Prior to the appearance of the Langmuir circulations, the depth of the shear layer scales with (vt)(1/2) (v is the kinematic viscosity and t is time), in accordance with molecular rather than turbulent transport. For final wind speeds in the range 3 to 5 m s(-1), the wavenumber of the most unstable Langmuir circulation normalized by the surface wavenumber, k(lc)*, is 0.68 +/- 0.24, at a reciprocal Langmuir number, La-1, of 52 +/- 21. The observations are compared with available theoretical results, although none are directly applicable to the conditions of the experiments. The implications of this work for the generation and evolution of Langmuir circulations in the ocean and other natural water bodies are discussed.

We present a study of nonlinear gravity-capillary waves with surface forcing and viscous dissipation. Based on a viscous boundary layer approximation near the water surface, the theory permits the efficient calculation of steady gravity-capillary waves with parasitic capillary ripples. To balance the viscous dissipation and thus achieve steady solutions, wind forcing is applied by adding a surface pressure distribution. For a given wavelength the properties of the solutions depend upon two independent parameters: the amplitude of the dominant wave and the amplitude of the pressure forcing. We find two main classes of waves for relatively weak forcing: Class 1 and Class 2. (A third class of solution requires strong forcing and is qualitatively different.) For Class 1 waves the maximum surface pressure occurs near the wave trough, while for Class 2 it is near the crest. The Class 1 waves are associated with Miles' (1957, 1959) mechanism of wind-wave generation, while the Class 2 waves may be related to instabilities of the subsurface shear current. For both classes of waves, steady solutions are possible only for forcing amplitudes greater than a certain threshold. We demonstrate how parasitic capillary ripples affect the dissipative and dispersive properties of the solutions. In particular, there may be a significant deviation from the linear phase speed for gravity-capillary waves. Also, wave damping is strongly enhanced by the parasitic capillaries (by as much as two orders of magnitude when compared to the case with no capillary waves). Preliminary experimental results from a wind-wave channel give good agreement with the theory. We find a sharp cut-off in the wavenumber spectra of the solutions which is similar to that observed in laboratory measurements of short gravity-capillary waves. Finally, for large wave amplitudes we find a sharp corner in the wave profile which may separate an overhanging wave crest from a train of parasitic capillaries.

Wave breaking at the surface of the ocean entrains bubbles, significantly modifying the phase speed and attenuation of acoustic waves propagating through the resulting two-phase medium. An autonomous buoy system was developed that directly measures sound speed at 3.33, 5, and 10 kHz at seven depths ranging from 0.7 to 7 m through the use of a travel-time technique. Simultaneous measurements at each depth are obtained at a 2-Hz rate, allowing observation of the unsteady sound-speed field from individual bubble injection events, as well as the calculation of mean sound speeds. The travel-time technique allows a direct measurement of the sound speed, eliminating the uncertainties common with inferring sound speeds from bubble population data. The sound speed buoy was deployed in the North Atlantic during the winter of 1993-94 as part of the Acoustic Surface Reverberation Experiment (ASREX). Our aim was to characterize the highly variable near-surface sound-speed field under varying environmental conditions. Forty-three days of data were obtained divning several storm cycles with wind speeds and significant wave heights reaching 20 m/s and 8 m, respectively. During periods of intense wave breaking, average sound speeds below 1000 m/s were observed at the 0.7-m measurement depth while instantaneous sound speeds during individual events approached values as low as 300 m/s. Furthermore, the data suggest that the dispersive effects of bubbles may extend to frequencies as low as 5 kHz near the surface during storms. Strong correlations of the mean and rms sound speed with the overlying wind and wave fields were found. (C) 1997 Acoustical Society of America.

Laboratory measurements of microwave scattering at grazing incidence from superposed wind and weakly nonlinear (AK<0.024) regular long waves are presented, This study is an extension of previous measurements with wind waves only, A dual polarized (VV, HH) coherent pulsed Ku-band (14 GHz) scatterometer with temporal resolution of 3 ns was used to obtain Doppler spectra and the absolute cross section of scattered signals for grazing angles from 6 degrees to 25 degrees and winds in the range 2-12 m/s, A wire wave-gauge array was used to measure the wind-wave field. Measurements of the frequency and amplitude modulation of the scattered signal due to the long waves showed that the data separated into two groups, The first grouping corresponded to HH scattering in the upwind direction and was clearly associated with scattering from the dominant gravity wind-waves on the crests of the long waves, In this case, the wind speed clearly influences the frequency modulation due to long waves. The second grouping corresponded to scattering in the downwind direction and was consistent with Bragg scattering from higher frequency waves, In this case the frequency modulation due to orbital velocity of the long waves was found to be weakly dependent on wind speed over the range of parameters studied. This classification of the electromagnetic scattering was consistent with comparisons of direct and Doppler measurements of the kinematics of the surface wave field.

We consider three-dimensional hydraulic jumps (shocks) propagating along boundaries in rotating fluids. This study is motivated by earlier work (Fedorov & Melville 1995), which dealt with the evolution to breaking of nonlinear Kelvin waves. We obtain the jump relations and derive an evolution equation for the jump as it propagates along the boundary. It is shown that after some initial adjustment the Kelvin-type jump assumes a permanent form and propagates with a constant velocity along the boundary or the coast. At some distance offshore the jump becomes oblique to the coastline, and the final shape of the jump and its speed depend only on the jump strength. The jump gives rise to a moderate mass transport offshore. The potential vorticity remains almost constant across the jump. The energy loss in the jump is proportional to the third power of the jump amplitude, which is similar to classical two-dimensional hydraulic jumps in non-rotating fluids. Jump properties are discussed for both weak and strong nonlinearity, and the role of a boundary layer region behind the leading edge of the jump is considered.

Breaking serves to limit the height of surface waves, mix the surface waters, generate ocean currents, and enhance air-sea fluxes of heat, mass, and momentum through the generation of turbulence and the entrainment of air. Breaking may result from intrinsic instabilities of deep-water waves or through wave-wave, wave-current, and wind-wave interactions. Observations in the field are made difficult by the fact that breaking is a strongly nonlinear intermittent process occurring over a wide range of scales. Controlled laboratory studies of breaking have proven useful in measuring the scaling relationships between the surface wave field and the kinematics and dynamics of breaking. Our inability to predict the occurrence and dynamics of breaking is a major impediment to the development of better wind-wave and mixed-layer models. Modern acoustic and electromagnetic oceanographic instrumentation should lead to significantly improved measurements of breaking in the near future.

The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to breaking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in the absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the Bow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast decays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.

Laboratory measurements of Ku-band scattering at grazing incidence are presented. This study was motivated by the need to understand the processes which significantly contribute to scattering at grazing incidence, A dual polarized (VV, HH) coherent pulsed Ku-band scatterometer with good temporal resolution (3 ns) was used to obtain Doppler spectra and the absolute cross-section of scattered signals for grazing angles from 6-12 degrees, and winds in the range 212 m/s. Wire wave gauges were used to measure the wind:wave field. Measurements of the first few moments of the Doppler spectra (cross-section, central frequency and bandwidth) showed that the data separated into two groups. The first grouping corresponded to HH scattering in the upwind look direction, and was clearly associated with scattering from the dominant gravity wind-waves, The second grouping corresponded to HH scattering in the downwind look direction, and all VV scattering, and was consistent with Bragg scattering from free higher frequency waves, This classification of the electromagnetic scattering was consistent with comparisons of direct and Doppler measurements of the kinematics of the surface wave field, The electromagnetic classification was also consistent with asymmetries in the wave field which increased with increasing wind speed.

Air bubbles entrained by breaking waves in the ocean surface layer can dramatically alter the velocity and attenuation of acoustic waves. The development of an effective technique for directly measuring the sound speed near the ocean surface is reported, The method makes use of the travel time of short acoustic pulses between a transmitter and a receiver separated by 40 cm. Phase distortions caused by acoustic reflections from the surface or from nearby buoy structural elements are separated in time from the direct path signal. A DSP-based data processing system was implemented to cross correlate the transmitted and received acoustic pulses and thus yield sound-speed measurements in real time. Perhaps the most significant novelty of the present measurement technique is its ability to make simultaneous measurements of the sound speed at several depths, starting as close as 0.5 m to the surface, at frequencies down to 5 kHz, and at a sample rate of 4 Hz per channel. Furthermore, the technique is direct and thus avoids the many difficulties involved with inferring the sound speed from in situ bubble population measurements. Results from controlled tests in the laboratory and in a lake are presented. The results confirm the validity of the technique and establish basic performance criteria. Data from the field that demonstrate the operation of the instrument in an ocean environment are also presented.

Measurements of the ambient noise spectrum level N with simultaneous, coincident wind and wave measurements were made from RP FLIP in fall 1991. The measurements were designed to investigate the correlation between the ambient noise and relevant surface wave parameters. The results suggest that wave parameters related to the incidence of wave breaking correlated well with the ambient noise level. The correlation between N and the rms wave amplitude a was found to be poor but that between N and the rms amplitude of the local wind sea a(w) was comparable to that between wind speed U and N. Similar good correlations were found between the rms wave slope s and N, and the higher frequency surface wave spectral levels and N. Correlations between the surface wave dissipation estimates D based on the Hasselmann and Phillips models and the ambient noise were comparable to those between the wind speed and the ambient noise. The mean square acoustic pressure was found to be proportional to D-n with n in the range 0.5-0.8. The implications of these results for monitoring surface waves and air-sea fluxes are discussed.

The electromagnetic (EM) bias epsilon is an error present in radar altimetry of the ocean surface due to nonuniform reflection with surface displacement. The electromagnetic bias is defined as the difference in height between the mean reflecting surface and the mean sea surface. A knowledge of the electromagnetic bias is required for reducing errors in mean sea level measurements by satellite radar altimeters, Direct measurements of the EM bias at 14 GHz (Ku band) and 5 GHz (C band) were made from an oil production platform in the Gulf of Mexico over a 6-month period during 1989 and 1990. A total of 1280 hours of usable data was collected, During the experiment the significant wave height (SWH) varied from 0.6 to 3.2 m; the wind speed at 25 m above the surface varied from 0.1 to 14.3 m s(-1): the Ku band bias varied from -1.0 to -13.8 cm, or from -1.6% to -5.3% of the SWH; and the C band bias varied from -0.4 to -19.9 cm, or from -0.6% to -6.3% of the SWH. The biases had mean values of -3.7% and -3.6% of SWH with standard deviations of the variability about the mean of 0.7% and 1.0% of SWH for Ku and C bands, respectively. We found a nonlinear relationship between dimensionless bias (bias/SWH) and wind speed at both low and high wind speeds. For wind speeds less than 3-4 m s(-1), both biases were found to be approximately constant. For wind speeds greater than 3-4 m s(-1) but less than 10 m s(-1), both biases were found to increase linearly with wind speed. For wind speeds greater than 11-12 m s(-1), the C band bias reaches a maximum. The Ku band bias reaches a maximum and then begins to decrease for wind speeds greater than 9-10 m s(-1).

Recent field measurements by Agrawal et al. have provided evidence of a shallow surface mixed layer in which the rate of dissipation due to turbulence is one to two orders of magnitude greater than that in a comparable turbulent boundary layer over a rigid wall. It is shown that predictions by Phillips of the energy lost by breaking surface waves in an equilibrium regime and laboratory measurements by Rapp and Melville of the mixing and turbulence due to breaking together lead to estimates of the enhanced dissipation rate and the thickness of the surface layer consistent with the field measurements. Wave-age-dependent scaling of the dissipation layer is proposed. Laboratory measurements of dissipation rates in both unsteady and quasi-steady breaking waves are examined. It is shown that an appropriately defined dimensionless rate of dissipation in unsteady breaking waves is not constant, but increases with a measure of the wave slope. Differences between dissipation rate in quasi-steady and unsteady breakers are discussed. It is found that measurements of the dissipation rate in unsteady breakers are consistent with independent estimates of the turbulent dissipation. The application of these results to models of dissipation due to breaking and air-sea fluxes is discussed.

Recent field and laboratory experiments have confirmed that low-frequency sound (10 to 300 Hz) is generated under breaking waves. It has been proposed that collective oscillations of the bubble plume generated by breaking may be the mechanism responsible for the generation of this sound. Confirmation of this process requires independent measurement of the void fraction, and therefore sound speed, in the bubbly mixture. Detailed measurements are presented of the evolution of the void-fraction field in bubble plumes generated by large-scale three-dimensional (3-D) laboratory breaking waves. Various moments of the void-fraction field are calculated and compared with results from two-dimensional (2-D) laboratory breaking waves [Lamarre and Melville, Nature 351, 469-472 (1991)]. The kinematics of the bubble plume reveals that the initial horizontal velocity of the plume is approximately 0.7C, where C is the wave phase speed. The centroid of the bubble plume is found to deepen at a speed of approximately 0.2H/T, where H and Tare the wave height at breaking and the wave period, respectively. The radial dependence of the void-fraction and sound-speed field is characterized in terms of simple functions of time. Finally, the void-fraction measurements described here, along with independent measurements of the pressure fluctuations under breaking waves [Loewen and Melville, J. Acoust. Soc. Am. 95, 1329-1343 (1994)], support the hypothesis that low-frequency sound is generated by the collective oscillations of the bubble plume.

Laboratory measurements of the sound produced by mechanically generated two-dimensional (2-D) and three-dimensional (3-D) breaking waves are presented. In the 2-D breaking experiments it was observed that the mean-square pressure at frequencies below 1 kHz correlated strongly with the fractional energy dissipated by breaking and the volume of air entrained. In addition, the volume of air entrained was found to be proportional to the fractional energy dissipated. These results imply that measurements of the low-frequency sound may be useful for studying the dynamics of breaking waves in the field. It was found that 2-D plunging breakers produced significant increases in spectral levels at frequencies below approximately 500 Hz but that spilling breakers did not. Large-amplitude low-frequency signals were observed to begin up to 1/3 of a wave period after the start of active breaking in both the two- and three-dimensional experiments. It is believed that these signals were due to the collective oscillation of the entrained bubble plumes. A model of a cylindrically shaped plume. located immediately below the free surface and the void-fraction measurements of Lamarre and Melville [J. Acoust. Soc. Am. 95, 1317-1328 (1994)] were used to compute the eigenfrequencies of the volume mode of collective oscillation. The computed eigenfrequencies closely matched the frequencies of the observed signals. This agreement between the experimental observations and theory provides considerable support for the hypothesis that the observed bubble plumes were oscillating collectively in their volume mode. This leads to the conclusion that the collective volume oscillations of bubble plumes entrained by breaking waves may be a source of low-frequency sound in the ocean.

The modulated nonlinear Schrodinger equation (Zhang & Melville 1990), describing the evolution of a weakly nonlinear short-gravity-wave train riding on a longer finite-amplitude gravity-wave train is used to study the stability of steady envelope solutions of the short-wave train. The formulation of the stability problem reduces to the solution of a pair of coupled equations for the disturbance amplitude and (relative) phase. Approximate analytical solutions and numerical solutions show that the conventional sideband (Benjamin-Feir) instability is just the first in a series of resonantly unstable regions which increase in number with increasing perturbation wavenumber. The first of these new instabilities is the result of a quintet resonance between four short waves and one long wave. Subsequent unstable regions correspond to sextet or higher-order resonances. The results presented here suggest that steady envelope solutions for unforced irrotational short waves on longer irrotational gravity waves may be unstable for a wide range of conditions.

We consider the general problem of geostrophic adjustment in a channel in the weakly nonlinear and dispersive (non-hydrostatic) limit. Governing equatio s of Boussinesq-type are derived, based on the assumption of weak nonlinear, dispersive and rotational effects, both for surface waves on a homogeneous fluid and internal waves in a two-layer system. Numerical solutions of the Boussinesq equations are presented, giving examples of the geostrophic adjustment in a c annel for two different kinds of initial disturbances, both with non-zero perturbation potential vorticity. The timescales of rotational separation (that is, the separation of the Kelvin and Poincare waves due to their dispersive properties) and that of nonlinear evolution are considered, with particular concern for the resonant interactions of nonlinear Kelvin waves and linear Poincare, waves described by Melville, Tomasson & Renouard (1989). A parameter measuring the ratio of the two timescales is used to predict when the free and forced Poincare waves may be separated in the solution. It also distinguishes the cases in which the linear solutions are valid for the rotational separation from those requiring the full Boussinesq equations. Finally, solutions for the evolution of nonlinear internal waves in a sea strait are presented, and the effects of friction on the wavefront curvature of the nonlinear Kelvin waves are briefly considered.

Laboratory measurements of the pressure distributions on surface-piercing vertical cylinders due to breaking waves are presented. Breaking waves are generated in a repeatable fashion under program control, and both vertical and azimuthal distributions of pressures were measured over many repeats of the experiments. Despite the repeatability of the controllable experimental conditions, it is found that the highest impact pressures are subject to considerable variability, including pressure oscillations, from run to run. This high impact region is found to be localized in space and time, and the variability is attributed to the random dynamics of the breaking wave front and the entrapped air. Thus, despite the repeatability of the upstream incident wave hydrodynamics, it appears that the prediction of the largest pressures is essentially a stochastic problem. For those aspects of flow-structure interaction which do not depend on the higher-frequency impact pressures, these experimental results may be extrapolated to full scale through the use of the pressure impulse.

We report on the development and use of an impedance probe to measure the volume fraction of air (void-fraction) in bubble plumes generated by breaking waves. The void-fraction gauge described here is found to be most useful in the initial period after breaking when large void-fractions prevail. We describe the instrumentation at length and report on its use in the laboratory and in the field. The instrument is found to be capable of rendering the space-time evolution of the void-fraction field from controlled laboratory breaking waves. Field results show measurements of void-fractions (up to 24%) which are several orders of magnitude greater than time averaged values previously reported [1], [2]. Preliminary measurements show that the fraction of breaking waves per wave, based on the detection of breaking by the void-fraction gauge, is dependent on significant wave height and wind speed. The dependence on wind speed is compared with data of previous investigators [3]. Underwater video photography from the field clearly shows the formation and evolution of distinct bubble plumes and the presence of large bubbles (at least 6-mm radius) generated by breaking.

We consider the waves generated by transcritical flow past a constriction in a channel, or by ships or surface pressure distributions travelling at transcritical speeds. The two-dimensionality of the upstream advancing nonlinear waves, which has been observed both experimentally and numerically by several authors, is described by a modal decomposition of the flow response. We show that the lowest transverse mode may evolve nonlinearly, leading to a two-dimensional response upstream, with the higher transverse modes swept downstream. This description is supported by comparing the initial evolution of the solutions to the corresponding linear and nonlinear problems. Averaging across the channel demonstrates that the three-dimensional problem may be related to the corresponding two-dimensional problem with an additional effective forcing coming from the nonlinear coupling of the higher modes to the lowest two-dimensional mode. This coupling leads to a dependence of the upstream solutions on the channel width as well as the Froude number. Solutions are also obtained for two-layer fluids in which cubic nonlinearity is also important. The inclusion of cubic nonlinearity permits the generation of two-dimensional fronts upstream, and demonstrates that the transition from three- to two-dimensional solutions upstream is not specific to Boussinesq solitary waves.

The sound produced from a single bubble, oscillating at its breathing mode frequency, and the bubble size distribution are used to model the sound produced by breaking waves. The data of Medwin and Daniel [J. Acoust. Soc. Am. 88, 408-412 (1990)] is used to evaluate the performance of the model. The model generates a damped sinusoidal pulse for every bubble formed, as calculated from the bubble size distribution. If the range from the receiver to the breaker is known then the only unknown parameters are epsilon, the initial fractional amplitude of the bubble oscillation, and L, the dipole moment arm. It is found that if the product epsilon x L is independent of the bubble radius the model reproduces the shape and magnitude of their measured sound spectrum accurately. The success of this simple model implies that the inverse problem (calculation of the bubble size distribution from the sound power spectrum) may be solved without the need to explicitly identify individual bubble pulses in the acoustic time series.

WAVE breaking transfers momentum from the atmosphere (winds) to the ocean (currents) 1,2 and entrains air in bubbles which are believed to generate and scatter underwater sound 3-5. Wave breaking and the associated entrainment of air in bubbles are also thought to be important in heat and gas transfer across the air-sea interface 6-8, but the lack of detailed measurements of air entrainment in bubbles has impeded our understanding of the effect of wave breaking on these processes. Here we present measurements of air entrainment by controlled deep-water breaking waves, which show that the bubble plumes generated by breaking waves contain volume fractions of air that are many orders of magnitude greater than expected. Bubble plumes with such large void fractions may be the source of low-frequency sound in the ocean 9. We conclude that the processes of surface-wave evolution and air entrainment are dynamically coupled, and that the contribution of bubbles to air-sea gas transfer and to sound propagation may be seriously underestimated if the existence of these plumes of large bubbles is not taken into account.

An experimental study of the microwave backscatter and acoustic radiation from breaking waves is reported. It is found that the averaged microwave and acoustic measurements correlate with the dynamics of wave breaking. Both the mean-square acoustic pressure and the backscattered microwave power correlate with the wave slope and dissipation, for waves of moderate slope (S < 0.28). The backscattered power and the mean-square pressure are also found to correlate strongly with each other. As the slope and wavelength of the breaking wave packet is increased, both the backscattered power and the mean-square pressure increase. It is found that a large portion of the backscattered microwave power precedes the onset of sound production and visible breaking. This indicates that the unsteadiness of the breaking process is important and that the geometry of the wave prior to breaking may dominate the backscattering. It is observed that the amount of acoustic energy radiated by an individual breaking wave scaled with the amount of mechanical energy dissipated during breaking. These laboratory results are compared to the field experiments of Farmer & Vagle (1988), Crowther (1989) and Jessup et al. (1990).