Showing papers on "Breaking wave published in 2010"

Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

Abstract: New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spect...

Dynamics of Winds and Currents Coupled to Surface Waves

Abstract: We discuss the coupling processes between surface gravity waves and adjacent winds and currents in turbulent boundary layers. These processes mediate exchanges of momentum, heat, and gases between the atmosphere and ocean and thus are of global significance for climate. Surface waves grow primarily by pressure-form stress from airflow over the waveforms, and they dissipate in the open sea by wave breaking that injects and stirs momentum, energy, and bubbles into the ocean. Wave motions pump wind eddies that control fluxes across the lower atmosphere. Flow separation occurs behind steep wave crests, and at high winds the crests flatten into spume, which diminishes the drag coefficient. In the ocean the Lagrangian-mean wave velocity, Stokes drift, induces a vortex force and material transport. These generate Langmuir circulations penetrating throughout the boundary layer and enhancing entrainment at the stratified interior interface in combination with other turbulent eddies and inertial-shear instability.

Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation. Fabrice ArdhuinJean-Francois Filipot and Rudy Magne Service Hydrographique et Oceanographique de la Marine, Brest, France

Abstract: New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, swell dissipation is nonlinear and proportional to the swell steepness, and wave breaking only affects spectral components such that the non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to long wave breaking is introduced, together with a reduction of wind-wave generation term for short waves, otherwise taken from Janssen (J. Phys. Oceanogr. 1991). These parameterizations are combined and calibrated with the Discrete Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but the parameterizations probably yield the most accurate overall estimate of wave parameters to date. Perspectives for further improvement are also given.

Depth-integrated, non-hydrostatic model with grid nesting for tsunami generation, propagation, and runup

Abstract: This dissertation describes the formulation, verification, and validation of a dispersive wave model with a shock-capturing scheme, and its implementation for basin-wide evolution and coastal runup of tsunamis using two-way nested computational grids. The depth-integrated formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. The semi-implicit, finite difference solution captures flow discontinuities associated with bores or hydraulic jumps through a momentum conservation scheme, which also accounts for energy dissipation in the wave breaking process without the use of an empirical model. An upwind scheme extrapolates the free surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This eliminates depth extrapolation errors and greatly improves the model stability, which is essential for computation of energetic breaking waves and runup. The vertical velocity term associated with non-hydrostatic pressure also describes tsunami generation and transfer of kinetic energy due to dynamic seafloor deformation. A depth-dependent Gaussian function smooths bathymetric features smaller than the water depth to improve convergence of the implicit, non-hydrostatic solution. A two-way grid-nesting scheme utilizes the Dirichlet condition of the non-hydrostatic pressure and both the velocity and surface elevation at the grid interface to ensure propagation of dispersive waves and discontinuities through computational grids of different resolution. The inter-grid boundary can adapt to topographic features to model wave transformation processes at optimal resolution and computational efficiency. The computed results show very good agreement with data from previous laboratory experiments for wave propagation, transformation, breaking, and runup over a wide range of conditions. The present model is applied to the 2009 Samoa Tsunami for demonstration and validation. These case studies confirm the validity and effectiveness of the present modeling approach for tsunami research and impact assessment. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models.

Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean

Abstract: Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the...

On internal wave breaking and tidal dissipation near the centre of a solar-type star

Abstract: We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star, primarily using two-dimensional numerical simulations based on a cylindrical model. A train of internal gravity waves is excited by tidal forcing at the interface between the convection and radiation zones of such a star. We derive a Boussinesq-type model of the central region of a star and find a non-linear wave solution that is steady in the frame rotating with the angular pattern speed of the tidal forcing. We then use spectral methods to integrate the equations numerically, with the aim of studying at what amplitude the wave is subject to instabilities. These instabilities are found to lead to wave breaking whenever the amplitude exceeds a critical value. Below this critical value, the wave reflects perfectly from the centre of the star. Wave breaking leads to mean flow acceleration, which corresponds to a spin-up of the central region of the star, and the formation of a critical layer, which acts as an absorbing barrier for subsequent ingoing waves. As these waves continue to be absorbed near the critical layer, the star is spun up from the inside out. Our results point to an important amplitude dependence of the (modified) tidal quality factor Q′, since non-linear effects are responsible for dissipation at the centre of the star. If the amplitude of the tidal forcing exceeds the critical amplitude for wave breaking to occur, then this mechanism produces efficient dissipation over a continuous range of tidal frequencies. This requires , for a planet of mass mp in an orbit of period P around the current Sun, neglecting stellar rotation. However, this criterion depends strongly on the strength of the stable stratification at the centre of the star, and so it depends on stellar mass and main-sequence age. If breaking occurs, we find , for the current Sun. This varies by no more than a factor of 5 throughout the range of solar-type stars with masses between 0.5 and 1.1 M⊙, for fixed orbital parameters. This estimate of Q′ is therefore quite robust and can be reasonably considered to apply to all solar-type main-sequence stars, if this mechanism operates. The strong frequency dependence of the resulting dissipation means that this effect could be very important in determining the fate of close-in giant planets around G and K stars. We predict fewer giant planets with orbital periods of less than about 2 d around such stars if they cause breaking at the centre, due to the efficiency of this process. Even if the waves are of too low amplitude to initiate breaking, radiative damping could, in principle, lead to a gradual spin-up of the stellar centre and to the formation of a critical layer. This process could provide efficient tidal dissipation in solar-type stars perturbed by less massive companions, but it may be prevented by effects that resist the development of differential rotation. These mechanisms would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.

Breaking of shoaling internal solitary waves

Abstract: The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes (S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes (S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope (Sw = a/Lw, where Lw is a measure of half of the wavelength) versus S space, and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number (Rew) on R, boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers (Rew ~ 104) were found to trigger a global instability, which modifies the breaking process relative to the lower Rew case, but not necessarily the breaking location, and results in a ~ 10 % increase in R, relative to the Rew ~ 103 case.

Direct-simulation-based study of turbulent flow over various waving boundaries

Abstract: We use direct numerical simulation of stress-driven turbulent Couette flows over waving surfaces to study turbulence in the vicinity of water waves. Mechanistic study is performed through systematic investigation of different wavy surface conditions including plane progressive Airy and Stokes waves with and without wind-induced surface drift, as well as stationary wavy walls and vertically waving walls for comparison. Two different wave steepness values ak = 0.1 and 0.25 are considered, where a is the wave amplitude and k is the wavenumber. For effects of wave age, defined as the ratio between the wave phase speed c and the turbulence friction velocity u*, we consider three values, namely c/u* = 2, 14 and 25, corresponding to slow, intermediate and fast waves, respectively. Detailed analysis of turbulence structure and statistics shows their dependence on the above-mentioned parameters. Our result agrees with previous measurement and simulation results and reveals many new features unreported in the literature. Over progressive waves, although no apparent flow separation is found in mean flow, considerable intermittent separations in instantaneous flow are detected in slow waves with large steepness. The near-surface coherent vortical structures are examined. We propose two conceptual vortex structure models: quasi-streamwise and reversed horseshoe vortices for slow waves and bent quasi-streamwise vortices for intermediate and fast waves. Detailed examination of Reynolds stress with quadrant analysis, turbulent kinetic energy (TKE) and TKE budget with a focus on production shows large variation with wave phase; analysis shows that the variation is highly dependent on wave age and wave nonlinearity. Comparison between Airy waves and Stokes waves indicates that although the nonlinearity of surface water waves is a high-order effect compared with the wave age and wave steepness, it still makes an appreciable difference to the turbulence structure. The effect of wave nonlinearity on surface pressure distribution causes substantial difference in the wave growth rate. Wind-induced surface drift can cause a phase shift in the downstream direction and a reduction in turbulence intensity; this effect is appreciable for slow waves but negligible for intermediate and fast waves. In addition to providing detailed information on the turbulence field in the vicinity of wave surfaces, the results obtained in this study suggest the importance of including wave dynamics in the study of wind–wave interaction.

Reanalysis of regular and random breaking wave statistics

Abstract: Statistics of breaking waves across the surf zone are reanalyzed on the basis of various sets of field and laboratory data so as to provide coastal engineers with reliable information on breaking w...

Simulation of storm surge, wave, currents, and inundation in the Outer Banks and Chesapeake Bay during Hurricane Isabel in 2003: The importance of waves

Abstract: [1] This paper investigates the effects of waves on storm surge, currents, and inundation in the Outer Banks and Chesapeake Bay during Hurricane Isabel in 2003 through detailed comparison between observed wind, wave, surge, and inundation data and results from an integrated storm surge modeling system, CH3D-SSMS. CH3D-SSMS, which includes coupled coastal and basin-scale storm surge and wave models, successfully simulated measured winds, waves, storm surge, currents, and inundation during Isabel. Comprehensive modeling and data analysis revealed noticeable effects of waves on storm surge, currents, and inundation. Among the processes that represent wave effects, radiation stress (outside the estuaries) and wave-induced stress (outside and inside the estuaries) are more important than wave-induced bottom stress in affecting the water level. Maximum surge was 3 m, while maximum wave height was 20 m offshore and 2.5 m inside the Chesapeake Bay, where the maximum wave-induced water level reached 1 m. Significant waves reached 3.5 m and 16 s at Duck Pier, North Carolina, and 1.6 m and 5 s at Gloucester, Virginia. At Duck, wave effects accounted for ∼36 cm or 20% of the peak surge elevation of 1.71 m. Inside the Chesapeake Bay, wave effects account for 5–10% of observed peak surge level. A two-layer flow is found at Kitty Hawk, North Carolina, during the peak of storm surge owing to the combined effects of wind and wave breaking. Higher surge elevations result when the 3-D surge model, instead of the 2-D surge model, is coupled with the 2-D wave model owing to its relatively lower bottom friction. Wave heights obtained with 3- and 2-D surge models show little difference.

Wave setup over a Pacific Island fringing reef

Abstract: [1] Measurements obtained across a shore-attached, fringing reef on the southeast coast of the island of Guam are examined to determine the relationship between incident waves and wave-driven setup during storm and nonstorm conditions. Wave setup on the reef flat correlates well (r > 0.95) and scales near the shore as approximately 35% of the incident root mean square wave height in 8 m water depth. Waves generated by tropical storm Man-Yi result in a 1.3 m setup during the peak of the storm. Predictions based on traditional setup theory (steady state, inviscid cross-shore momentum and depth-limited wave breaking) and an idealized model of localized wave breaking at the fore reef are in agreement with the observations. The reef flat setup is used to estimate a similarity parameter at breaking that is in agreement with observations from a steeply sloping sandy beach. A weak (∼10%) increase in setup is observed across the reef flat during wave events. The inclusion of bottom stress in the cross-shore momentum balance may account for a portion of this signal, but this assessment is inconclusive as the reef flat currents in some cases are in the wrong direction to account for the increase. An independent check of fringing reef setup dynamics is carried out for measurements at the neighboring island of Saipan with good agreement.

On internal wave breaking and tidal dissipation near the centre of a solar-type star

Abstract: We study the fate of internal gravity waves, which are excited by tidal forcing by a short-period planet at the interface of convection and radiation zones, approaching the centre of a solar-type star. We study at what amplitude these wave are subject to instabilities. These instabilities lead to wave breaking whenever the amplitude exceeds a critical value. Below this value, the wave reflects perfectly from the centre of the star. Wave breaking results in spinning up the central regions of the star, and the formation of a critical layer, which acts as an absorbing barrier for ingoing waves. As these waves are absorbed, the star is spun up from the inside out. This results in an important amplitude dependence of the tidal quality factor Q'. If the tidal forcing amplitude exceeds the value required for wave breaking, efficient dissipation results over a continuous range of tidal frequencies, leading to Q' \approx 10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of 5 throughout the range of G and K type main sequence stars, for a given orbit. We predict fewer giant planets with orbital periods of less than about 2 days around such stars, if they cause breaking at the centre, due to the efficiency of this process. This mechanism would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.

Modeling wave impact on salt marsh boundaries

Abstract: [1] Wind-wave attack is the fundamental cause of erosion of salt marsh boundaries. Tidal forcing acts as a proxy determining at which elevation waves pound against the marsh edge and conditioning the propagation and transformation of wave trains as they move toward these boundaries. The objective of the present work is to evaluate, through analysis of the results of a numerical model, the effect of wave action on marsh boundaries as a function of tidal elevation and wave height for different edge configurations. In order to link numerical simulations to field conditions, the model inputs are based on topographical and hydrodynamical surveys conducted at a study site at the Virginia Coast Reserve (VCR), VA. Model results show that the wave thrust on the marsh scarp strongly depends on tidal level. The thrust increases with tidal elevation until the marsh is submerged and then rapidly decreases. The wave thrust is maximum for a vertical scarp and minimum for a terraced scarp. Similarly, wave energy dissipation is maximized just above the marsh platform elevation, when wave reflection is reduced and wave breaking occurs at the marsh edge.

Wave-Breaking Model for Boussinesq-Type Equations Including Roller Effects in the Mass Conservation Equation

Abstract: We investigate the ability of a 1D fully nonlinear Boussinesq model including breaking to reproduce surf zone waves in terms of wave height and nonlinear intraphase properties such as asymmetry and skewness. An alternative approach for wave-breaking parameterization including roller effects through diffusive-type terms on both, the mass conservation and momentum equations is developed and validated on regular wave and solitary wave experiments as an attempt to improve wave height and left-right asymmetry estimates. The new approach is able to reproduce wave height decay, and intraphase nonlinear properties within the entire surf zone of spilling breakers without requiring temporal evolution of model parameters.

Temporal observations of rip current circulation on a macro-tidal beach

Abstract: A field experiment was conducted on a high energy macro-tidal beach (Perranporth, UK) to examine rip current dynamics over a low-tide transverse bar/rip system in response to changing tide and wave conditions. Hydrodynamic data were collected using an array of in situ acoustic doppler current meters and pressure transducers, as well as 12 GPS-tracked Lagrangian surf zone drifters. Inter-tidal and subtidal morphology were measured through RTK-GPS and echo-sounder surveys. Data were collected for eight consecutive days (15 tides) over a spring-neap tidal cycle with tidal ranges of 4‐6.5m and offshore significant wave heights of 1‐2m and peak periods of 5‐12s. The hypothesis that rip current dynamics in a macro-tidal setting are controlled by the combination of variations in wave dissipation and morphological flow constriction, modulated by changes in tidal elevation was tested. During the measurement period, rip circulation was characterised by a large rotational surf zone eddy O(200m) extending offshore from the inner-surf zone to the seaward face of the inter-tidal transverse bar. During high- and mid-tide, water depth over the bars was too deep to allow wave breaking, and a strong longshore current dominated the surf zone. As the water depth decreased towards low-tide, wave breaking was concentrated over the bar crests initiating the rotational rip current eddy. Peak rip flow speeds of 1.3ms ! 1 were recorded around low-tide when the joint effects of dissipation and morphological constriction were maximised. At low tide, dissipation over the bar crests was reduced by partial bar-emergence and observations suggested that rip flows were maintained by morphological constriction and the side-drainage of water from the transverse bars.

Maximum steepness of oceanic waves: Field and laboratory experiments

Abstract: The breaking of waves is an important mechanism for a number of physical, chemical and biological processes in the ocean. Intuitively, waves break when they become too steep. Unfortunately, a general consensus on the ultimate shape of waves has not been achieved yet due to the complexity of the breaking mechanism which still remains the least understood of all processes affecting waves. To estimate the limiting shape of ocean waves, here we present a statistical analysis of a large sample of individual wave steepness. Data were collected from measurements of the surface elevation in laboratory facilities and the open sea under a variety of sea state conditions. Observations reveal that waves are able to reach steeper profiles than the Stokes' limit for stationary waves. Due to the large number of records this finding is statistically robust. Copyright © 2010 by the American Geophysical Union.

Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model

Abstract: An experimental study of energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model to simulate the dissipation due to wave breaking are reported in this paper. Measured wave surface elevations are used to examine the characteristic time and length scales associated with wave groups and local breaking waves, and to estimate and parameterize the energy dissipation and dissipation rate due to wave breaking. Numerical tests using the eddy viscosity model are performed and we find that the numerical results well capture the measured energy loss. In our experiments, three sets of characteristic time and length scales are defined and obtained: global scales associated with the wave groups, local scales immediately prior to breaking onset and post-breaking scales. Correlations among these time and length scales are demonstrated. In addition, for our wave groups, wave breaking onset predictions using the global and local wave steepnesses are found based on experimental results. Breaking time and breaking horizontal length scales are determined with high-speed imaging, and are found to depend approximately linearly on the local wave steepness. The two scales are then used to determine the energy dissipation rate, which is the ratio of the energy loss to the breaking time scale. Our experimental results show that the local wave steepness is highly correlated with the measured dissipation rate, indicating that the local wave steepness may serve as a good wave-breaking-strength indicator. To simulate the energy dissipation due to wave breaking, a simple eddy viscosity model is proposed and validated with our experimental measurements. Under the small viscosity assumption, the leading-order viscous effect is incorporated into the free-surface boundary conditions. Then, the kinematic viscosity is replaced with an eddy viscosity to account for energy loss. The breaking time and length scales, which depend weakly on wave breaking strength, are applied to evaluate the magnitude of the eddy viscosity using dimensional analysis. The estimated eddy viscosity is of the order of 10 −3 m 2 s −1 and demonstrates a strong dependence on wave breaking strength. Numerical simulations with the eddy viscosity estimation are performed to compare to the experimental results. Good agreement as regards energy dissipation due to wave breaking and surface profiles after wave breaking is achieved, which illustrates that the simple eddy viscosity model functions effectively.

Real-time simulation of large bodies of water with small scale details

Abstract: We present a hybrid water simulation method that combines grid based and particles based approaches. Our specialized shallow water solver can handle arbitrary underlying terrain slopes, arbitrary water depth and supports wet-dry regions tracking. To treat open water scenes we introduce a method for handling non-reflecting boundary conditions. Regions of liquid that cannot be represented by the height field including breaking waves, water falls and splashing due to rigid and soft bodies interaction are automatically turned into spray, splash and foam particles. The particles are treated as simple non-interacting point masses and they exchange mass and momentum with the height field fluid. We also present a method for procedurally adding small scale waves that are advected with the water flow. We demonstrate the effectiveness of our method in various test scene including a large flowing river along a valley with beaches, big rocks, steep cliffs and waterfalls. Both the grid and the particles simulations are implemented in CUDA. We achieve real-time performance on modern GPUs in all the examples.

Strong Turbulence in the Wave Crest Region

Abstract: High-resolution vertical velocity profiles in the surface layer of a lake reveal the turbulence structure beneath strongly forced waves. Dissipation rates of turbulence kinetic energy are estimated based on centered second-order structure functions at 4-Hz sampling. Dissipation rates within nonbreaking wave crests are on average 3 times larger than values found at the same distance to the free surface but within the wave trough region. This ratio increases to 18 times for periods with frequent wave breaking. The depth-integrated mean dissipation rate is a function of the wave field and correlates well with the mean wave saturation in the wave band ωp ≤ ω ≤ 4ωp. It shows a clear threshold behavior in accordance with the onset of wave breaking. The initial bubble size distribution is estimated from the observed distribution of energy dissipation rates, assuming the Hinze scale being the limiting size. This model yields the slope of the size distribution, , consistent with laboratory results reporte...

Observations of Wave Breaking Kinematics in Fetch-Limited Seas

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 met

Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water

Abstract: The paper extends a pilot study into a detailed investigation of properties of breaking waves and processes responsible for breaking. Simulations of evolution of steep to very steep waves to the point of breaking are undertaken by means of the fully nonlinear Chalikov–Sheinin model. Particular attention is paid to evolution of nonlinear wave properties, such as steepness, skewness and asymmetry, in the physical, rather than Fourier space, and to their interplay leading to the onset of breaking. The role of superimposed wind is also investigated. The capacity of the wind to affect the breaking onset is minimal unless the wind forcing is very strong. Wind is, however, important as a source of energy for amplification of the wave steepness and ultimately altering the breaking statistics. A detailed laboratory study is subsequently described. The theoretical predictions are verified and quantified. In addition, some features of the nonlinear development not revealed by the model (i.e. reduction of the wave period which further promotes an increase in steepness prior to breaking) are investigated. Physical properties of the incipient breaker are measured and examined, as well as characteristics of waves both preceding and following the breaker. The experiments were performed both with and without a superimposed wind, the role of which is also investigated. Since these idealized two-dimensional results are ultimately intended for field applications, tentative comparisons with known field data are considered. Limitations which the modulational instability mechanism can encounter in real broadband three-dimensional environments are highlighted. Also, substantial examination of existing methods of breaking onset detection are discussed and inconsistencies of existing measurements of breaking rates are pointed out.

Wave-turbulence interaction and its induced mixing in the upper ocean

Abstract: [1] In the ocean, interaction among the mean current, the surface waves, and turbulence is a major mechanism for energy transfer from surface waves to the turbulence field. This process is associated with attenuation of surface waves. This paper deals with wave-turbulence interaction and its induced mixing using field observations and a one-dimensional, level 2.5 turbulence closure model. The results show that both the turbulence kinetic energy dissipation rate and the vertical mixing induced by wave-turbulence interaction are a function of us0u*2 and wave parameters, where us0 is the Stokes drift at the sea surface and u* is the friction velocity in water. The former decays with the depth away from the surface in the form of e2kz, while the latter decays as e3kz (k is the wave number). We also analyze the wave decay induced by wave-turbulence interaction. The decay time scale is in proportion to cL/u*2, while in inverse proportion to , where c is a phase speed, L is a wavelength, and δ is a wave steepness. A series of numerical experiments are performed to evaluate the effects of wave-turbulence interaction. The results from the cases with effects of wave-turbulence interaction show significant improvement in simulation of turbulence characteristics compared to the cases in the absence of surface waves. This implies that wave-turbulence interaction is a significant mechanism for generation of turbulence kinetic energy in the upper ocean and plays an important role in regulating vertical mixing and surface wave decay.

Dynamics of steep two-dimensional gravity-capillary solitary waves

Abstract: In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.