Breaking Wind Waves Research Articles

Experimental study on the variation characteristics of focused wave packets with wave spectra scaled from different stages of wave growth

This study investigated the relationship between wave breaking and spectral evolution, focusing on the variations in wave spectra caused solely by breaking under different initial spectral shapes. Laboratory experiments utilizing a controlled wave focusing technique were conducted to generate breaking wave trains with input spectra derived from SWAN model simulations representing 12 distinct stages of wave growth under varying wind durations. Experiment data were combined with HOS simulations to isolate the breaking spectral changes from nonlinearity. Results reveal that the Benjamin-Feir instability dominates the nonlinear interactions for young waves, exhibiting an asymmetric shift towards higher wavenumbers. The characteristics of breaking-induced spectral changes depend on the initial spectral shape and consistent with the “two-phase behavior” of wind wave breaking. The study reveals new insights into the increase in the low-frequency energy, finding that this gain was primarily associated with the breaking of dominant waves near the spectral peak, whereas high-frequency breaking played a minimal role in transferring energy towards lower frequencies. A strong correlation between Qp and the proportion of spectral dissipation in different frequency ranges was revealed, suggesting that Qp can serve as a valuable parameter for characterizing the spectral evolution of breaking waves at various stages of development.

Influence of wind and waves on ambient noise and bubble entrainment depth in the semi-enclosed Baltic Sea

Semi-enclosed, fetch-limited waters create unique conditions for wind wave development and breaking. Parameters of breaking waves influence bubble entrainment depth and associated noise, which is why they differ in semi-enclosed sea compared to open waters. While the established noise-wind speed relationship holds in oceanic conditions, it differs in land-constrained basins like the Baltic Sea. To explore noise level, bubble entrainment depth and wind speed relationships, we conducted noise and sub-surface bubble measurements, coupled with wind observations, in the selected area of the Baltic Sea during two consecutive summers. A novel method was employed to estimate bubble entrainment depth under conditions of strong backscatter. Model data of wave field parameters were employed to assess their influence on noise level and bubble entrainment depth. Results suggest stronger connections between noise level and wind speed, as well as wave height, compared to wave age and wind sea steepness. The same patterns hold true for the correlation between bubble entrainment depth and both wind speed and wave field parameters. The parameterized noise level-wind speed relationship differs from that obtained for oceanic conditions and also varies across measurement periods. Observed differences were shaped by varying wind-wave conditions, notably differences in wind speed, direction, wave height, and the presence of swell. The noise level-bubble entrainment depth relation is reported for the first time for Baltic Sea conditions. For a thorough analysis of the influence of these factors on noise and bubbles, longer measurements under diverse wind-wave conditions are required to account for site-specific wave field characteristics.

Modeling surface wave dynamics in upper Delaware Bay with living shorelines

Living shorelines gain increasing attention because they stabilize shorelines and reduce erosion. This study leverages physics-based models and bagged regression tree (BRT) machine learning algorithm to simulate wave dynamics at a living shoreline composed of constructed oyster reefs (CORs) in upper Delaware Bay. The physics-based models consist of coupled Delft3D-FLOW and SWAN in four-level nested domains. The model accuracy converges with increasing mesh resolution. The simulated wave-induced current circulation substantiates the effectiveness of CORs in trapping sediments. The simulated yearly-averaged wave power correlates qualitatively with historical shoreline retreat rates. BRT is adopted to improve the model accuracy, identify key processes responsible for simulation errors in wave height (Hs) and wave period (Tp), and quantify their importance. In the CORs sheltered area, BRT reveals that simulation errors of wind seas mainly arise from wind forcing, wave breaking and wave triad interactions. Wave breaking is seven times more important than wind forcing for simulating Hs, while wind forcing and triad interactions are of equal importance for simulating Tp. Simulation errors of swells mostly stem from bottom friction and offshore wave boundary conditions. Results from this study can help the assessment and adaptive management of CORs-based living shoreline restoration projects under climate change.

Estimation of the “whitecap” lifetime of breaking wave

The paper presents the results of a study of the lifetime of wind-wave breaking (“whitecaps”) and the spatial distribution of the moments of wave-breaking initiation along the profile of a long surface wave. The results obtained during the specialized experiments from an oceanographic platform in the Black Sea are given. The registration of the whitecaps was carried out based on the video recordings of the sea surface. The surface waves’ characteristics were measured and the meteorological information was recorded simultaneously with the video recordings. It is shown that the distribution of the whitecaps’ lifetime is well described by an exponential law. It was found that the ratio of the lifetime of an individual whitecap to the period of the breaking wave is 0.3. The distributions of the above-mentioned ratio are similar for different wind and wave conditions. It is indicated that the generation of whitecaps occurs mainly in the region of the crest of a long wave with a shift to its front slope on average by 9.6 of the phase of the long wave. The whitecap having arisen at the leading edge shifts to the trailing edge of the long wave during its lifetime, so that the phase difference between the breaking initiation and the maximum of the surface fraction covered by the whitecaps equals 21.6.

2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

AbstractA fully consistent 2D parametric model of wave development under spatially and/or time varying winds is developed. Derived coupled equations are written in their characteristic form to provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are developing and distributed under varying wind forcing conditions. For young waves, nonlinear interactions drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are governing the wave energy evolution. With a prescribed wind wave growth rate, proportional to (u*/c) squared, wave breaking dissipation must follow a power‐function of the dominant wave slope. For uniform wind conditions, this choice for the growth rate imposes solutions to follow fetch laws, with exponents q = −1/4, p = 3/4 correspondingly. This set of exponents recovers the Toba's laws, and imposes the wave breaking exponent equal to 3. A varying wind direction can then drive spectral peak direction changes, leading to the occurrence of focusing/defocusing wave groups over localized areas where wave‐rays merge and cross. Significant (but finite) local variations of the energy are then expected under varying wind forcing. Propagating away from a stormy area, wave rays generally diverge, leading to dispersive swell systems. Examples of practical applications of this model are provided in (Kudryavtsev et al., 2021, companion paper).

Simultaneous Observations of Turbulent Reynolds Stress in the Ocean Surface Boundary Layer and Wind Stress over the Sea Surface

AbstractThis study used high‐frequency acoustic instruments mounted on an offshore observation platform to obtain simultaneous in situ measurements of sea surface winds and ocean currents. The acquired data were used to compare quantitatively the turbulent Reynolds stress in the ocean surface boundary layer (OSBL) and the wind stress over the sea surface. During the study period (∼10 d), the sea state was largely dominated by swell and breaking wind waves. The eddy covariance method was used to estimate the two stresses. A combination of the synchrosqueezed wavelet transform (SWT) method and a moving average was employed for wave‐turbulence decomposition of the oceanic velocities. Results showed that the turbulent Reynolds stress in the OSBL is affected greatly by surface gravity waves and that it scales with the wave characteristics. Direct comparison revealed that the turbulent Reynolds stress in the OSBL could be larger than the wind stress in certain circumstances, which differs from the traditional view that the former cannot be greater than the latter. In certain extreme cases, their ratio can be up to one order of magnitude. Therefore, we conclude that surface waves can enhance significantly the turbulent Reynolds stress in the OSBL.

Features of Profiles for Currents, Momentum Flux, and a Turbulence Dissipation Rate in Wind-Wave Channel

Vertical profiles of the mean horizontal currents U(z), the vertical momentum fluxes τ(z), and the turbulence kinetic-energy dissipation rates (TKE dissipation rate) e(z) in the upper water layer (UWL) are considered and their joint analysis is carried out. For this purpose, data from laboratory measurements performed in the wind-wave channel of the Institute of Applied Physics, Russian Academy of Sciences (RAS) [1, 2], are used. They correspond to conditions of strong wind and breaking wind waves. The profiles of the currents and momentum fluxes are estimated for x and z components of the velocity at five horizons in the UWL at four various wind values. The empirical estimates of e(z) obtained from the same data in the previous work [3] are used in the joint analysis. It is established that (a) velocity of currents U(z) increases noticeably when compared to the values of U(z) in the absence of waves, (b) the momentum flux in the water τw(z) decreases noticeably when compared to that in the air τa(z), and (c) τw(z) significantly attenuates with depth according to ratio τw(z) ~ 1/z2. The mentioned anomalies of profiles U(z) and τ(z) in the UWL are analyzed together with the previously determined pattern of TKE dissipation-rate falloff with depth according to ratio e(z) ~ 1/z2 in order to search for an interpretation of the results.

A New Approach for Modeling Dissipation due to Breaking in Wind Wave Spectra

AbstractA robust spectral dissipation term for wind waves has long been a goal of detailed-balance spectral modeling and is represented by many different approximations in spectral models of random wave fields. A Monte Carlo approach is employed here to create a random-phase sea surface that is used to simulate the distribution of horizontal surface velocities at the sea surface and to relate these velocities to deep-water wind wave breaking. Results are consistent with many recent studies that show a kinematic-based breaking criterion can provide a consistent depiction of the onset of wave breaking. This criterion is combined with the calculated nonlinear flux rates to estimate a transition point within a spectrum at which a spectrum changes from an f−4 equilibrium-range form to an f−5 region dominated by dissipation, potentially an important factor within several air–sea interaction mechanisms, turbulence at the sea surface, and remote sensing applications. It also has the potential to improve operational modeling capabilities.

Field observation of wave reflection from plunging cliff coasts of Chabahar

In this study, a linear formulation is found to estimate the wave reflection coefficient (Kr) from plunging cliff coasts of Chabahar city according to field data measurements. The field measurement included directional wave data via three bursts for each hour and in total 1345 bursts during summer Southern-West monsoon using an ADCP gague. The significant wave heights reached 2.5 m and the corresponding peak periods were greater than 11 s.It was observed that the wave reflection coefficients are fully tidally modulated. The maximum values of Kr reached 0.7 in a flood period of spring tide, while the minimum values were greater than 0.3 and corresponded to ebb periods in spring tide. The corresponding dimensionless parameters of wave height to depth, wave steepness and Ursell number to the highest values of Kr were obtained as 0.17, 0.014, and 22, respectively. The variation ranges of reflection coefficient pertaining to the effect of four main tidal constituents as M2, S2, K1, and O1 were achieved as ∼ 9.6, 4.1, 7.1, and 3.6%, respectively. Finally, a linear formulation as a function of the tidal level was resulted to estimate the most accurate values of Kr in the studied area. The averaged inaccuracy of resulted formulation was approximately 6.5%.The frequency reflection coefficients Kr(f) was also investigated in this study. The results indicated the values close to 1 for long infragravity waves, because of occurrence of no significant dissipation. However, the similar values for short waves (fr > 0.25 Hz) were greater than 1 due to wind wave breaking as a result of the cliff toe collision. The temporal histogram of Kr(f) revealed the tidally controlled variations of this parameter.

Marine Aerosol Production via Detrainment of Bubble Plumes Generated in Natural Seawater With a Forced‐Air Venturi

AbstractDuring September–October 2016, a marine aerosol generator configured with forced‐air Venturis was deployed at two biologically productive and two oligotrophic regions of the western North Atlantic Ocean to investigate factors that modulate primary marine aerosol (PMA) production. The generator produced representative bubble size distributions with Hinze scales (0.32 to 0.95 mm radii) and void fractions (0.011 to 0.019 Lair Lsw‐1) that overlapped those of plumes produced in the surface ocean by breaking wind waves. Hinze scales and void fractions of bubble plumes varied among seawater hydrographic regions, whereas corresponding peaks and widths of bubble size distributions did not, suggesting that variability in seawater surfactants drove variability in plume dynamics. Peaks in size‐resolved number production efficiencies for model PMA (mPMA) emitted via bubble bursting in the generator were within a narrow range (0.059 to 0.069 μm geometric mean diameter) over wide ranges in subsurface bubble characteristics, suggesting that subsurface bubble size distributions were not the primary controlling factors as was suggested by previous work. Total mass production efficiencies for mPMA decreased with increasing air detrainment rates, supporting the hypothesis that surface bubble rafts attenuate mPMA mass production. Total mass and Na+ production efficiencies for mPMA from biologically productive seawater were significantly greater than those from oligotrophic seawater. Corresponding mPMA number distributions peaked at smaller sizes during daytime, suggesting that short‐lived surfactants of biological and/or photochemical origin modulated diel variability in marine aerosol production.

Centrifuge modelling of breaking waves and seashore ground

Seashore ground stability is a crucial issue in the composite problems of hydraulics and geotechnics. Many studies have been conducted on covering materials and sediment transport. However, very few studies have examined this issue from a geotechnical viewpoint. This is because the ground displays complicated responses against breaking waves, and because it is difficult to examine ground behaviours through a prototype-scale model test. The physical modelling of breaking wind waves and seashore ground helps explain ground stability. This study examined the efficacy of centrifuge modelling with regard to this issue. The authors showed the similarity laws, including fluid behaviours and developed a new wave generator. The centrifuge model efficacy was verified mainly by way of the modelling of model tests on waveform, wave height and water pressure on and in the ground. Additional tests indicated that excess pore-water pressure was generated due to wave set-up. Increasing the wave height and/or wave frequency caused a seepage force, which could decrease ground stability.

Observation-Based Source Terms in the Third-Generation Wave Model WAVEWATCH III: Updates and Verification

AbstractThe observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E(f) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f−4 to a power law of about f−5, comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E(f) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E(f) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%.

Profile features of dissipation rates of turbulence in Lake Taihu and possible mechanism

湍流不仅是导致物质、动量等在水-气交界面的交换、水柱内部输送的关键过程，也是促进浅水湖泊中底泥再悬浮及水生生态系统演变的驱动力；其中湍流动能耗散率（ε）不仅是描述湍流动能变化的关键物理量，也是刻画水体中湍流产生机制的关键过程.基于2017年10月29日-11月2日位于太湖梅梁湾采集的高频三维流速廓线和水温廓线观测资料，结合东山气象站同期的风场和辐射等气象资料，探讨太湖中ε的分布特征及其变化的可能机制.结果表明，0.7 m深度以下水平方向上ε介于10^-8~10^-7 m²/s³之间，比垂直方向大一个数量级左右.尽管大型浅水湖泊几何深度浅，但其ε的深度廓线依然存在典型的3层：ε随深度递减的风浪直接作用层，深度从水面至1.0 m左右；ε基本不随深度变化的常数层，分布区间为水深1.0~1.9 m；随后是ε随深度递减的底边界混合层.热力分层的强弱（垂向温差）、位置对常数层和底部边界中ε的贡献显著，甚至造成ε的常数层起始深度下移.本研究有利于进一步理解大型浅水湖泊的动力学过程及其对水生生态系统演变的驱动效应.;Turbulence is a key process regulating the exchange of matter and momentum not only across the water-gas interface, but also within water columns. It is also a driving force for the resuspension of sediments and the evolution of shallow lake ecosystems. The dissipation rate of the turbulent kinetic energy (ε) is a key physical quantity which depicts the evolution of the turbulent kinetic energy, and discriminates turbulence production rate from mechanisms in water bodies. Based on observations for profiles of three-dimensional currents using Acoustic Doppler Current Profiles (ADCP) and records on water temperature and the wind field in Lake Taihu from October 29, 2017 to November 2, 2017, the profile features of ε in this large-scale shallow lake were explored. The horizontal ε is about 10^-8-10^-7 m²/s³ below 0.7 m water depth, about one order of magnitude larger than the vertical ε. Despite the shallowness of the lake, there are still three typical layers of ε for u',v', and w':the wind-wave layer, where the water depth is shallower than 1.0 m, exhibits that ε decreases with depth due to wind forcing, Langmuir turbulence and wave breaking; constant layer, in the range of 1.0 m to 1.9 m or so, shows that ε is little variation with the depth; bottom boundary mixed layer, below the constant layer, exhibits that ε decreases with depth. In Lake Taihu, the strength and location of stratification significantly contribute to ε in the constant layer and the bottom boundary, and even cause the initial depth of the constant layer of ε to move downward. This study will help to further understand the kinetic process of large shallow lakes and their evolutionary effects on aquatic ecosystems.

Organic Matter in the Surface Microlayer: Insights From a Wind Wave Channel Experiment

The surface microlayer (SML) is the uppermost thin layer of the ocean and influencing interactions between the air and sea, such as gas exchange, atmospheric deposition and aerosol emission. Organic matter (OM) plays a key role in air-sea exchange processes, but studying how the accumulation of organic compounds in the SML relates to biological processes is impeded in the field by a changing physical environment, in particular wind speed and wave breaking. Here, we studied OM dynamics in the SML under controlled physical conditions in a large annular wind wave channel, filled with natural seawater, over a period of 26 days. Biology in both SML and bulk water was dominated by bacterioneuston, and -plankton, respectively, while autotrophic biomass in the two compartments was very low. In general, SML thickness was related to the concentration of dissolved organic carbon (DOC) but not to enrichment of DOC or of specific OM components in the SML. Pronounced changes in OM enrichment and molecular composition were observed in the course of the study and correlated significantly to bacterial abundance. Thereby, hydrolysable amino acids, in particular arginine, were more enriched in the SML than combined carbohydrates. Amino acid composition indicated that less degraded organic matter accumulated preferentially in the SML. A strong correlation was established between the amount of surfactants coverage and -aminobutric acid, suggesting that microbial cycling of amino acids can control physiochemical traits of the SML. Our study shows that accumulation and cycling of OM in the SML can occur independently of recent autotrophic production, indicating a widespread biogenic control of process across the air-sea exchange.

Relationship between turbulent energy dissipation and gas transfer through the air–sea interface

The nonlinear dependence of gas transfer velocity on wind speed typically results in the best fit of observational data; however, gas transfer velocity is dimensionally inconsistent with the nonlinear wind speeds. The objective of the current study was to show that, in the case of wind waves, gas transfer velocity with a consistent dimension should be determined by turbulent viscosity instead of by the viscosity of water when parameterised using the renewal model. Turbulent kinetic energy (TKE) near the air–sea interface is significantly intensified by breaking wind waves. By analyzing various models, we found that the TKE dissipation rate was explicitly linearly related to wind speed and dependent on wave age, with powers ranging from –2.36 to 4.0. Various models show that wave energy dissipation (WED) due to wind wave breaking explicitly increases with the cube of the wind speed and weakly depends on wave age. Assuming a balance between WED and total TKE dissipation in a constant dissipation layer, the depth of this layer was shown to be comparable to the wave height. Using the traditional renewal model with wind wave turbulent viscosity and TKE dissipation rate at the sea surface, we found that the gas transfer velocity was explicitly linearly related to wind speed in a dimensionally consistent manner, and depended simultaneously on the wave age and drag coefficient. These results are consistent with observational data obtained using the eddy correlation method. We emphasise that the linear dependence on wind speed is only valid when the wave age and drag coefficient are fixed; thus, this finding cannot be directly confirmed by currently available observational data due to a lack of wave state information.

Effects of wave-current interaction on storm surge in the Taiwan Strait: Insights from Typhoon Morakot

The effects of wave-current interaction on storm surge are investigated by a two-dimensional wave-current coupling model through simulations of Typhoon Morakot in the Taiwan Strait. The results show that wind wave and slope of sea floor govern wave setup modulations within the nearshore surf zone. Wave setup during Morakot can contribute up to 24% of the total storm surge with a maximum value of 0.28m. The large wave setup commonly coincides with enhanced radiation stress gradient, which is itself associated with transfer of wave momentum flux. Water levels are to leading order in modulating significant wave height inside the estuary. High water levels due to tidal change and storm surge stabilize the wind wave and decay wave breaking. Outside of the estuary, waves are mainly affected by the current-induced modification of wind energy input to the wave generation. By comparing the observed significant wave height and water level with the results from uncoupled and coupled simulations, the latter shows a better agreement with the observations. It suggests that wave-current interaction plays an important role in determining the extreme storm surge and wave height in the study area and should not be neglected in a typhoon forecast.

Coherent motions and time scales that control heat and mass transfer at wind-swept water surfaces

Forecast of the heat and chemical budgets of lakes, rivers and oceans requires improved predictive understanding of air-water interfacial transfer coefficients. Here we present laboratory observations of the coherent motions that occupy the air-water interface at wind speeds (U10) 1.1 to 8.9 m/s. Spatio-temporal near-surface velocity data and interfacial renewal data are made available by a novel flow tracer method. The relative activity, velocity scales and time scales of the various coherent interfacial motions are measured, namely for Langmuir circulations, streamwise streaks, non-breaking wind waves, parasitic capillary waves, non-turbulent breaking wind waves, and turbulence-generating breaking wind waves. Breaking waves exhibit a sudden jump in streamwise interfacial velocity wherein the velocity jumps up to exceed the wave celerity and destroys nearby parasitic capillary waves. Four distinct hydrodynamic regimes are found to exist between U10 = 0 and 8.9 m/s, each with a unique population balance of the various coherent motions. The velocity scales, time scales and population balance of the different coherent motions are input to a first-principles gas transfer model to explain the waterside transfer coefficient (kw) as well as experimental patterns of temperature and gas concentration. The model mixes concepts from surface renewal and divergence theories, and requires surface divergence strength (β), the Lagrangian residence time inside the upwelling zone (tLu), and the total lifetime of new interface before it is downwelled (tLT). The model's output agrees with time-averaged measurements kw, patterns of temperature in infrared photographs, and spatial patterns of gas concentration and kw from direct numerical simulations. Several non-dimensional parameters, e.g. βtLu and τstLT where τs is the interfacial shear rate, determine the effectiveness of a particular type of coherent motion for affecting kw. This article is protected by copyright. All rights reserved.

Mechanism of drag coefficient saturation at strong wind speeds

AbstractPrevious studies have demonstrated the saturation of drag coefficients at strong wind speeds. But the mechanism behind this saturation has not yet been fully clarified. In this study, at normal and strong wind speeds, we use a wind‐wave tank for investigating the peak enhancement factor of the wind‐sea spectrum, which is an appropriate wave parameter for representing interfacial flatness. We measured the water‐level fluctuation using wave gauges. At strong wind speeds, the result shows that the peak enhancement factor of the wind‐sea spectrum decreases with decreasing inverse wave age and with increasing wind speed. This suggests that the distinctive wind‐wave breaking occurs at strong wind speeds. It also suggests that this distinctive breaking of wind waves causes the saturation of drag coefficients at strong wind speeds.

The Sound of Tropical Cyclones

Abstract Underwater ambient sound levels beneath tropical cyclones were measured using hydrophones onboard Lagrangian floats, which were air deployed in the paths of Hurricane Gustav (2008) and Typhoons Megi (2010) and Fanapi (2010). The sound levels at 40 Hz–50 kHz from 1- to 50-m depth were measured at wind speeds up to 45 m s−1. The measurements reveal a complex dependence of the sound level on wind speed due to the competing effects of sound generation by breaking wind waves and sound attenuation by quiescent bubbles. Sound level increases monotonically with increasing wind speed only for low frequencies (<200 Hz). At higher frequencies (>200 Hz), sound level first increases and then decreases with increasing wind speed. There is a wind speed that produces a maximum sound level for each frequency; the wind speed of the maximum sound level decreases with frequency. Sound level at >20 kHz mostly decreases with wind speed over the wind range 15–45 m s−1. The sound field is nearly uniform with depth in the upper 50 m with nearly all sound attenuation limited to the upper 2 m at all measured frequencies. A simple model of bubble trajectories based on the measured float trajectories finds that resonant bubbles at the high-frequency end of the observations (25 kHz) could easily be advected deeper than 2 m during tropical cyclones. Thus, bubble rise velocity alone cannot explain the lack of sound attenuation at these depths.

Finite time blow-up and breaking of solitary wind waves.

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.