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- Author or Editor: W. Kendall Melville x

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## Abstract

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 rates 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.

## Abstract

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 rates 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.

## Abstract

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 braking. 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 de 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 flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays 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.

## Abstract

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 braking. 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 de 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 flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays 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.

## Abstract

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 he 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.

## Abstract

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 he 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.

## Abstract

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
} is the mean wave frequency and

## Abstract

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
} is the mean wave frequency and

## Abstract

Breaking waves play an important role in air–sea interaction, enhancing momentum flux from the atmosphere to the ocean, dissipating wave energy that is then available for turbulent mixing, injecting aerosols and sea spray into the atmosphere, and affecting air–sea gas transfer due to air entrainment. In this paper observations are presented of the occurrence of breaking waves under conditions of strong winds (10–25 m s^{−1}) and fetch-limited seas (0–500 km) in the Gulf of Tehuantepec Experiment (GOTEX) in 2004. An airborne nadir-looking video camera, along with a global positioning system (GPS) and inertial motion unit (IMU), provided digital videos of the breaking sea surface and position in an earth frame. In particular, the authors present observations of Λ(**c**), which is the distribution of breaking wave crest lengths per unit sea surface area, per unit increment in velocity **c** or scalar speed *c*, first introduced by O. M. Phillips. In another paper, the authors discuss the effect of processing methodology on the resulting shape of the Λ(**c**) distribution. In this paper, the elemental method of measuring breaking crests is used to investigate the Λ(**c**) distributions under a variety of wind and wave conditions. The integral and the first two moments of the Λ(**c**) distributions are highly correlated with the active breaking rate and the active whitecap coverage. The computation of whitecap coverage yields a larger observational dataset from which the variability of whitecap coverage with wind speed, friction velocity, wave age, and wave slope is presented and compared to previous observations. The dependence of the active breaking rate on the spectral peak steepness is in agreement with previous studies. Dimensional analysis of Λ(*c*) indicates that scaling with friction velocity and gravity, as in the classical fetch relations, collapses the breaking distributions more effectively than scaling with dominant wave parameters. Significant wave breaking is observed at speeds near the spectral peak in young seas only, consistent with previous studies. The fourth and fifth moments of Λ(*c*) are related to the flux of momentum transferred by breaking waves to the underlying water and the rate of wave energy dissipation, respectively. The maximum in the fourth moment occurs at breaking speeds of 5–5.5 m s^{−1}, and the maximum in the fifth moment occurs at 5.8–6.8 m s^{−1}, apparently independent of wave age. However, when nondimensionalized by the phase speed at the peak of the local wave spectrum *c _{p}
*, the maxima in the nondimensionalized fourth and fifth moments show a decreasing trend with wave age, obtaining the maxima at dimensionless speeds

*c*/

*c*near unity at smaller wave ages and moving to lower dimensionless speeds

_{p}*c*/

*c*≪ 1 at larger wave ages. The angular dependence of Λ(

_{p}**c**) is predominantly unimodal and better aligned with the wind direction than the dominant wave direction. However, the directional distribution of Λ(

**c**) is broadest for small

**c**and often exhibits a bimodal structure for slow breaking speeds under developing seas. An asymmetry in the directional distribution is also observed for moderately developed seas. Observations are compared to the Phillips model for Λ(

*c*) in the equilibrium range of the wave spectrum. Although the ensemble of Λ(

*c*) distributions appears consistent with a

*c*

^{−6}function, the distributions are not described by a constant power-law exponent. However, the Λ(

*c*) observations are described well by the Rayleigh distribution for slow and intermediate speeds, yet fall above the Rayleigh distribution for the fastest breaking speeds. From the Rayleigh description, it is found that the dimensionless width of the Λ(

*c*) distribution increases weakly with dimensionless fetch,

*s*/

*u*

_{*e }= 1.69

*χ*

^{0.06}, where

*s*is the Rayleigh parameter,

*u*

_{*e }is the effective friction velocity, and the dimensionless fetch

*X*and gravitational acceleration

*g*. The nondimensionalized total length of breaking per unit sea surface area is found to decrease with dimensionless fetch for intermediate to fully developed seas,

*A*is the total length of breaking crests per unit sea surface area.

## Abstract

Breaking waves play an important role in air–sea interaction, enhancing momentum flux from the atmosphere to the ocean, dissipating wave energy that is then available for turbulent mixing, injecting aerosols and sea spray into the atmosphere, and affecting air–sea gas transfer due to air entrainment. In this paper observations are presented of the occurrence of breaking waves under conditions of strong winds (10–25 m s^{−1}) and fetch-limited seas (0–500 km) in the Gulf of Tehuantepec Experiment (GOTEX) in 2004. An airborne nadir-looking video camera, along with a global positioning system (GPS) and inertial motion unit (IMU), provided digital videos of the breaking sea surface and position in an earth frame. In particular, the authors present observations of Λ(**c**), which is the distribution of breaking wave crest lengths per unit sea surface area, per unit increment in velocity **c** or scalar speed *c*, first introduced by O. M. Phillips. In another paper, the authors discuss the effect of processing methodology on the resulting shape of the Λ(**c**) distribution. In this paper, the elemental method of measuring breaking crests is used to investigate the Λ(**c**) distributions under a variety of wind and wave conditions. The integral and the first two moments of the Λ(**c**) distributions are highly correlated with the active breaking rate and the active whitecap coverage. The computation of whitecap coverage yields a larger observational dataset from which the variability of whitecap coverage with wind speed, friction velocity, wave age, and wave slope is presented and compared to previous observations. The dependence of the active breaking rate on the spectral peak steepness is in agreement with previous studies. Dimensional analysis of Λ(*c*) indicates that scaling with friction velocity and gravity, as in the classical fetch relations, collapses the breaking distributions more effectively than scaling with dominant wave parameters. Significant wave breaking is observed at speeds near the spectral peak in young seas only, consistent with previous studies. The fourth and fifth moments of Λ(*c*) are related to the flux of momentum transferred by breaking waves to the underlying water and the rate of wave energy dissipation, respectively. The maximum in the fourth moment occurs at breaking speeds of 5–5.5 m s^{−1}, and the maximum in the fifth moment occurs at 5.8–6.8 m s^{−1}, apparently independent of wave age. However, when nondimensionalized by the phase speed at the peak of the local wave spectrum *c _{p}
*, the maxima in the nondimensionalized fourth and fifth moments show a decreasing trend with wave age, obtaining the maxima at dimensionless speeds

*c*/

*c*near unity at smaller wave ages and moving to lower dimensionless speeds

_{p}*c*/

*c*≪ 1 at larger wave ages. The angular dependence of Λ(

_{p}**c**) is predominantly unimodal and better aligned with the wind direction than the dominant wave direction. However, the directional distribution of Λ(

**c**) is broadest for small

**c**and often exhibits a bimodal structure for slow breaking speeds under developing seas. An asymmetry in the directional distribution is also observed for moderately developed seas. Observations are compared to the Phillips model for Λ(

*c*) in the equilibrium range of the wave spectrum. Although the ensemble of Λ(

*c*) distributions appears consistent with a

*c*

^{−6}function, the distributions are not described by a constant power-law exponent. However, the Λ(

*c*) observations are described well by the Rayleigh distribution for slow and intermediate speeds, yet fall above the Rayleigh distribution for the fastest breaking speeds. From the Rayleigh description, it is found that the dimensionless width of the Λ(

*c*) distribution increases weakly with dimensionless fetch,

*s*/

*u*

_{*e }= 1.69

*χ*

^{0.06}, where

*s*is the Rayleigh parameter,

*u*

_{*e }is the effective friction velocity, and the dimensionless fetch

*X*and gravitational acceleration

*g*. The nondimensionalized total length of breaking per unit sea surface area is found to decrease with dimensionless fetch for intermediate to fully developed seas,

*A*is the total length of breaking crests per unit sea surface area.

## Abstract

The authors present airborne observations of fetch-limited waves during strong offshore winds in the Gulf of Tehuantepec. The measurements, collected over a wide range of fetches, include one- and two-dimensional surface wavenumber spectra and turbulent fluxes in winds up to 25 m s^{−1}. The evolution of the wave spectra is in good agreement with the fetch relationships from previous observations. The tails of the observed one-dimensional *k*
_{1} spectra, in the dominant wave direction, exhibit a *k*
_{1} spectrum is well parameterized with dependence on the effective fetch and friction velocity. At higher wavenumbers within the saturation range, although the one-dimensional saturation in the dominant wave direction is independent of the wind forcing, the saturation in the crosswind direction is weakly dependent on the effective wave age and on average 30% larger than that in the downwind direction. The results are discussed in the context of previous observations and current numerical wind-wave prediction models.

## Abstract

The authors present airborne observations of fetch-limited waves during strong offshore winds in the Gulf of Tehuantepec. The measurements, collected over a wide range of fetches, include one- and two-dimensional surface wavenumber spectra and turbulent fluxes in winds up to 25 m s^{−1}. The evolution of the wave spectra is in good agreement with the fetch relationships from previous observations. The tails of the observed one-dimensional *k*
_{1} spectra, in the dominant wave direction, exhibit a *k*
_{1} spectrum is well parameterized with dependence on the effective fetch and friction velocity. At higher wavenumbers within the saturation range, although the one-dimensional saturation in the dominant wave direction is independent of the wind forcing, the saturation in the crosswind direction is weakly dependent on the effective wave age and on average 30% larger than that in the downwind direction. The results are discussed in the context of previous observations and current numerical wind-wave prediction models.

## Abstract

During the Gulf of Tehuantepec Experiment (GOTEX), conducted in February 2004, surface-wave measurements were collected using a scanning lidar [Airborne Topographic Mapper (ATM)] on the National Science Foundation (NSF)/NCAR C-130 aircraft during fetch-limited conditions with winds speeds ranging from 10 to 25 m s^{−1}. The authors present direct comparisons between the observed evolution of the wave field and numerical simulations using a parameterization of the wave energy dissipation. For low and intermediate wavenumbers, the dissipation corresponds to the saturation-based parameterization by Alves and Banner. However, at higher wavenumbers, their formulation cannot maintain saturation of the spectrum. Here, the authors use a dissipation term that forces the spectrum to match the empirical degree of saturation and explicitly balances the wind input and the nonlinear energy fluxes. All model simulations were carried out with “exact” computations of the nonlinear energy transfer because of four-wave resonant interactions and two empirical wind input functions. There is a good agreement for the integral parameters between the observations and the simulations, with root-mean-square (rms) errors between 5% and 12%. The tail of the computed omnidirectional wavenumber spectrum *ϕ*(*k*) can be approximated by two ranges: an equilibrium range, where *ϕ* ∝ *k*
^{−5/2}, and a saturation range, where *ϕ* = *B*
*k*
^{−3}, where *B*
*ϕ* overestimates the energy with rms errors between 20% and 50%, and the computed spectra are found to be narrower than the observations by about 10°. Similarly, the modeled bimodal directional distributions, at wavenumbers higher than the spectral peak, exhibit lobe separations and amplitudes that are consistently smaller than the observations. The lobe separation of the bimodal directional distribution for all simulations approximately scales with the square root of the wave age, which is consistent with the observations. The reasons for differences between the measurements and the simulations are discussed.

## Abstract

During the Gulf of Tehuantepec Experiment (GOTEX), conducted in February 2004, surface-wave measurements were collected using a scanning lidar [Airborne Topographic Mapper (ATM)] on the National Science Foundation (NSF)/NCAR C-130 aircraft during fetch-limited conditions with winds speeds ranging from 10 to 25 m s^{−1}. The authors present direct comparisons between the observed evolution of the wave field and numerical simulations using a parameterization of the wave energy dissipation. For low and intermediate wavenumbers, the dissipation corresponds to the saturation-based parameterization by Alves and Banner. However, at higher wavenumbers, their formulation cannot maintain saturation of the spectrum. Here, the authors use a dissipation term that forces the spectrum to match the empirical degree of saturation and explicitly balances the wind input and the nonlinear energy fluxes. All model simulations were carried out with “exact” computations of the nonlinear energy transfer because of four-wave resonant interactions and two empirical wind input functions. There is a good agreement for the integral parameters between the observations and the simulations, with root-mean-square (rms) errors between 5% and 12%. The tail of the computed omnidirectional wavenumber spectrum *ϕ*(*k*) can be approximated by two ranges: an equilibrium range, where *ϕ* ∝ *k*
^{−5/2}, and a saturation range, where *ϕ* = *B*
*k*
^{−3}, where *B*
*ϕ* overestimates the energy with rms errors between 20% and 50%, and the computed spectra are found to be narrower than the observations by about 10°. Similarly, the modeled bimodal directional distributions, at wavenumbers higher than the spectral peak, exhibit lobe separations and amplitudes that are consistently smaller than the observations. The lobe separation of the bimodal directional distribution for all simulations approximately scales with the square root of the wave age, which is consistent with the observations. The reasons for differences between the measurements and the simulations are discussed.

## Abstract

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 flow. This leads to the resonant generation of equatorially trapped gravity–inertial (or Poincaré) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincaré 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.

## Abstract

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 flow. This leads to the resonant generation of equatorially trapped gravity–inertial (or Poincaré) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincaré 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.

## Abstract

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.

## Abstract

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.

## Abstract

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

## Abstract

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