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Showing papers on "Breaking wave published in 2009"


Journal ArticleDOI
TL;DR: In this paper, the wave energy balance is verified in a wide range of conditions and scales, from gentle swells to major hurricanes, from the global ocean to coastal settings using in situ and remote sensing data.
Abstract: New parameterizations for the spectra 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 observation 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 non-zero only when a 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 to represent the dissipation of short waves due to longer breaking waves. Several degrees of freedom are introduced in the wave breaking and the wind-wave generation term of 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 gentle swells to major hurricanes, 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 yield the best overall results to date. Perspectives for further improvement are also given.

420 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed modified MPS methods for the prediction of wave impact pressure on a coastal structure by introducing new formulations for the pressure gradient and a new formulation of the source term of the Poisson Pressure Equation (PPE).

288 citations


Journal ArticleDOI
TL;DR: In this article, a depth-integrated, non-hydrostatic model with a semi-implicit finite difference scheme was proposed to model weakly dispersive wave propagation, transformation, breaking, and run-up.
Abstract: This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. 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. Copyright © 2008 John Wiley & Sons, Ltd.

270 citations


Journal ArticleDOI
TL;DR: In this article, the surface current response to winds is analyzed in a 2-yr time series of a 12-MHz (HF) Wellen Radar (WERA) off the west coast of France.
Abstract: The surface current response to winds is analyzed in a 2-yr time series of a 12-MHz (HF) Wellen Radar (WERA) off the west coast of France. Consistent with previous observations, the measured currents, after filtering tides, are on the order of 1.0%–1.8% of the wind speed, in a direction 10°–40° to the right of the wind, and with systematic trends as a function of wind speed. This Lagrangian current can be decomposed as the vector sum of a quasi-Eulerian current UE, representative of the top 1 m of the water column and part of the wave-induced Stokes drift Uss at the sea surface. Here, Uss is estimated with an accurate numerical wave model using a novel parameterization of wave dissipation processes. Using both observed and modeled wave spectra, Uss is found to be very well approximated by a simple function of the wind speed and significant wave height, generally increasing quadratically with the wind speed. Focusing on a site located 100 km from the mainland, the wave-induced contribution of Uss ...

243 citations


Journal ArticleDOI
TL;DR: In this paper, an internal wave-maker method using a momentum source function was proposed for Navier-Stokes equations models and various numerical simulations in two and three dimensions were performed using the momentum source wavemaker applied to the RANS equation model.

201 citations


Journal ArticleDOI
TL;DR: Two independent, large scale experiments performed in two wave basins of different dimensions show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves.
Abstract: We discuss two independent, large scale experiments performed in two wave basins of different dimensions in which the statistics of the surface wave elevation are addressed. Both facilities are equipped with a wave maker capable of generating waves with prescribed frequency and directional properties. The experimental results show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves. Sea states characterized by long-crested and steep waves are more likely to be populated by freak waves with respect to those characterized by a large directional spreading.

197 citations


Journal ArticleDOI
TL;DR: The response of the circulation of a coral reef system in Kaneohe Bay, Hawaii, to incident wave forcing was investigated using field data collected during a 10-month experiment as mentioned in this paper.
Abstract: The response of the circulation of a coral reef system in Kaneohe Bay, Hawaii, to incident wave forcing was investigated using field data collected during a 10-month experiment. Results from the study revealed that wave forcing was the dominant mechanism driving the circulation over much of Kaneohe Bay. As predicted theoretically, wave setup generated near the reef crest resulting from wave breaking established a pressure gradient that drove flow over the reef and out of the two reef channels. Maximum reef setup was found to be roughly proportional to the offshore wave energy flux above a threshold root-mean-square wave height of 0.7 m (at which height setup was negligible). On the reef flat, the wave-driven currents increased approximately linearly with incident wave height; however, the magnitude of these currents was relatively weak (typically <20 cm s−1) because of (i) the mild fore-reef slope of Kaneohe Bay that reduced setup resulting from a combination of frictional wave damping and its re...

188 citations


Journal ArticleDOI
TL;DR: In this paper, a wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world, to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves.
Abstract: A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

180 citations


Journal ArticleDOI
Erik Wahlén1
TL;DR: In this article, the authors construct small-amplitude steady periodic water waves with constant vorticity, which do not exist in the irrotational setting, and give a full description of the particle paths.

178 citations


Journal ArticleDOI
TL;DR: In this paper, a coupled level set and volume-of-fluid (CLSVOF) method is implemented for the numerical simulations of interfacial flows in ship hydrodynamics.

170 citations


Journal ArticleDOI
TL;DR: A coupled wave-circulation numerical model was used to simulate the distribution of wave energy, as well as the circulation induced by wave breaking, wind, and tidal forcing, within a coral reef system in Kaneohe Bay, Oahu, Hawaii as discussed by the authors.
Abstract: [1] A coupled wave-circulation numerical model was used to simulate the distribution of wave energy, as well as the circulation induced by wave breaking, wind, and tidal forcing, within a coral reef system in Kaneohe Bay, Oahu, Hawaii. Modeled wave, current, and wave setup fields were compared with field measurements collected on the forereef, reef flat, and reef channels and in the lagoon over a 4-week period. The predicted wave height transformation across the reef-lagoon system was in good agreement with field observations, using single-parameter (spatially uniform) values to describe both wave-breaking and frictional dissipation. The spatial distribution of the resulting wave setup field drove a persistent wave-driven flow across the reef flat that returned to the ocean through two deeper channels in the reef. Both the magnitude and direction of these currents were well described using a spatially uniform hydraulic roughness length scale. Notably, the model lends support to field observations that setup within the coastally bounded lagoon was a substantial fraction of the maximum setup on the reef (∼60–80%), which generated relatively weak cross-reef wave-driven flows (∼10–20 cm s−1) compared with reefs having mostly unbounded lagoons (e.g., many atolls and barrier reefs). Numerical experiments conducted using Lagrangian particle tracking revealed that residence times within Kaneohe Bay are extremely heterogeneous, typically ranging from 1 month within its sheltered southern lagoon.

Journal ArticleDOI
TL;DR: In this paper, the simulation of two-phase flows using a volume of fluid (VOF) method, balanced-force surface tension and quad/octree adaptive mesh refinement (AMR) is presented.

Journal ArticleDOI
TL;DR: In this article, the evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator.
Abstract: The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < e < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect...

Journal ArticleDOI
TL;DR: In this paper, the effects of rotation and nonlinearity on the evolution of the internal tide in the South China Sea have been explored using time series measurements using inverted echo-sounders at three locations.
Abstract: Observations of internal waves travelling across the deep basin of the South China Sea provide an opportunity for exploring the effects of rotation and non‐linearity on their evolution. Time series measurements using inverted echo‐sounders at three locations illustrate the progressive steepening of the internal tide generated in Luzon Strait and the subsequent development of short non‐linear internal wave trains. Potential mechanisms for internal tide generation are discussed in terms of tidal beam interaction with near‐surface stratification and mode 1 response to flow over a ridge. For transformation of an internal tide under the influence of non‐linearity and rotation, we apply Boyd's (2005) criterion for wave stability in a rotating flow to separate waves dominated by non‐linearity, which can be expected to steepen and break, from waves that are inhibited from breaking due to rotational dispersion of energy into internal inertial gravity waves. Wave breaking in this context refers to the poin...

Journal ArticleDOI
TL;DR: In this article, the propagation of transient wave groups, focused at a point in time and space to produce locally large waves having a range of steepness, was studied in a wave flume at Dalian University of Technology.

Journal ArticleDOI
TL;DR: In this paper, the authors used particle image velocimetry to estimate the wave energy dissipation rate in the presence of isotropic turbulence in the case of 1.5-Hz deep-water waves.
Abstract: This paper is dedicated to wave-induced turbulence unrelated to wave breaking. The existence of such turbulence has been foreshadowed in a number of experimental, theoretical, and numerical studies. The current study presents direct measurements of this turbulence. The laboratory experiment was conducted by means of particle image velocimetry, which allowed estimates of wavenumber velocity spectra beneath monochromatic nonbreaking unforced waves. Observed spectra intermittently exhibited the Kolmogorov interval associated with the presence of isotropic turbulence. The magnitudes of the energy dissipation rates due to this turbulence in the particular case of 1.5-Hz deep-water waves were quantified as a function of the surface wave amplitude. The presence of such turbulence, previously not accounted for, can affect the physics of the wave energy dissipation, the subsurface boundary layer, and the ocean mixing in a significant way.

Journal ArticleDOI
TL;DR: In this paper, direct numerical simulations are employed to examine gravity wave instability dynamics at a high intrinsic frequency, wave amplitudes both above and below nominal convective instability, and a Reynolds number sufficiently high to allow a fully developed turbulence spectrum.
Abstract: Direct numerical simulations are employed to examine gravity wave instability dynamics at a high intrinsic frequency, wave amplitudes both above and below nominal convective instability, and a Reynolds number sufficiently high to allow a fully developed turbulence spectrum Assumptions include no mean shear, uniform stratification, and a monochromatic gravity wave to isolate fluxes due to gravity wave and turbulence structures from those arising from environmental shears or varying wave amplitudes The results reveal strong wave breaking for both wave amplitudes, severe primary wave amplitude reductions within ∼1 or 2 wave periods, an extended turbulence inertial range, significant excitation of additional wave motions exhibiting upward and downward propagation, and a net positive vertical potential temperature flux due to the primary wave motion, with secondary waves and turbulence contributing variable and negative potential temperature fluxes, respectively Turbulence maximizes within ∼1 buoya

Journal ArticleDOI
TL;DR: In this article, a simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface.
Abstract: Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

Journal ArticleDOI
TL;DR: In this article, an analysis of the potential vorticity gradient and the refractive index in quasigeostrophic (QG) flows on the sphere reveals that the absolute Vorticity and the stretching parts have two contradictory effects on the horizontal shape of the baroclinic waves when the full variations of the Coriolis parameter are taken into account in each term.
Abstract: An analysis of the potential vorticity gradient and the refractive index in quasigeostrophic (QG) flows on the sphere reveals that the absolute vorticity and the stretching parts have two contradictory effects on the horizontal shape of the baroclinic waves when the full variations of the Coriolis parameter are taken into account in each term. The absolute vorticity effect favors the anticyclonic (southwest–northeast) tilt and anticyclonic wave breaking (AWB) and is stronger in the upper troposphere. In contrast, the stretching effect promotes the cyclonic (northwest–southeast) tilt and cyclonic wave breaking (CWB) and is more efficient at lower levels. A positive eddy feedback acting on the latitudinal variations of the zonal winds is deduced. Because the absolute vorticity and the stretching effects are respectively more and less efficient with increasing latitude, a more northward (southward) jet renders AWB more (less) probable and CWB less (more) probable; the jet is pushed or maintained mor...

01 Jan 2009
TL;DR: In this paper, the authors used particle image velocimetry to estimate the wave energy dissipation rate in the presence of isotropic turbulence in the case of 1.5-Hz deep-water waves.
Abstract: This paper is dedicated to wave-induced turbulence unrelated to wave breaking. The existence of such turbulence has been foreshadowed in a number of experimental, theoretical, and numerical studies. The current study presents direct measurements of this turbulence. The laboratory experiment was conducted by means of particle image velocimetry, which allowed estimates of wavenumber velocity spectra beneath monochromatic nonbreaking unforced waves. Observed spectra intermittently exhibited the Kolmogorov interval associated with the presence of isotropic turbulence. The magnitudes of the energy dissipation rates due to this turbulence in the particular case of 1.5-Hz deep-water waves were quantified as a function of the surface wave amplitude. The presence of such turbulence, previously not accounted for, can affect the physics of the wave energy dissipation, the subsurface boundary layer, and the ocean mixing in a significant way.

Journal ArticleDOI
TL;DR: In this paper, an exact Riemann solver is developed to permit a finite-volume solution to the flow model with smallest possible local error. And the subsequent impact is modelled with a novel compressible-flow model for a homogeneous mixture of incompressible liquid and ideal gas.
Abstract: When an ocean wave breaks against a steep-fronted breakwater, sea wall or a similar marine structure, its impact on the structure can be very violent. This paper describes the theoretical studies that, together with field and laboratory investigations, have been carried out in order to gain a better understanding of the processes involved. The wave's approach towards a structure is modelled with classical irrotational flow to obtain the different types of impact profiles that may or may not lead to air entrapment. The subsequent impact is modelled with a novel compressible-flow model for a homogeneous mixture of incompressible liquid and ideal gas. This enables a numerical description of both trapped air pockets and the propagation of pressure shock waves through the aerated water. An exact Riemann solver is developed to permit a finite-volume solution to the flow model with smallest possible local error.The high pressures measured during wave impacts on a breakwater are reproduced and it is shown that trapped air can be compressed to a pressure of several atmospheres. Pressure shock waves, reflected off nearby surfaces such as the seabed, can lead to pressures comparable with those of the impact. Typical examples of pressure-time histories, force and impulse are presented and discussed in terms of their practical implications. The numerical model proposed is relevant for a variety of flows where air effects are important. Further applications, including extended studies of wave impacts, are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors examined the character, intermittency, and anisotropy of turbulence accompanying wave instability, breaking, and turbulence evolution and decay for gravity waves (GW) having a high intrinsic frequency, amplitudes above and below nominal convective instability, and a high Reynolds number.
Abstract: This paper examines the character, intermittency, and anisotropy of turbulence accompanying wave instability, breaking, and turbulence evolution and decay for gravity waves (GW) having a high intrinsic frequency, amplitudes above and below nominal convective instability, and a high Reynolds number. Wave breaking at both amplitudes leads to an extended inertial range of turbulence, with turbulence energies that maximize within ∼1 wave period of the onset of breaking. Turbulence sources include both shear and buoyancy, with shear being the major contributor. Turbulence displays considerable intermittency both within and across the phase of the breaking gravity wave and exhibits clear anisotropy throughout the evolution. Turbulence anisotropy is found at all spatial scales and all times but is most pronounced in the most statically stable phase of the GW and at late times as the turbulent flow restratifies.

Journal ArticleDOI
TL;DR: In this article, the role of the breaking intensity on the resulting flow was investigated using a two-fluids Navier-Stokes solver combined with a Level-Set technique for interface capturing.
Abstract: The flow generated by the breaking of free-surface waves of different initial steepnesses is simulated numerically. The aim is to investigate the role played by the breaking intensity on the resulting flow. The study, which assumes a two-dimensional flow, makes use of a two-fluids Navier–Stokes solver combined with a Level-Set technique for the interface capturing. The evolution of periodic wavetrains is considered. Depending on the initial steepness ϵ, the wavetrain remains regular or develops a breaking, which can be either of spilling or plunging type. From the analysis of the local strain fields it is shown that, in the most energetic phase of plunging breaking, dissipation is mainly localized about the small air bubbles generated by the fragmentation of the air cavity entrapped by the plunging of the jet. The downward transfer of the horizontal momentum is evaluated by integrating the flux of momentum through horizontal planes lying at different depths beneath the still water level. From weak to moderate breaking, increase in the breaking intensity results in growing transfer of horizontal momentum, as well as thickening of the surface layer. Beyond a certain breaking intensity, the larger amount of air entrapped causes a reduction in the momentum transferred and the shrinkage of the layer. Quantitative estimates of the amount of air entrapped by the breaking and of the degassing process are provided. A scaling dependence of the amount of air entrapped by the first plunging event on the initial steepness is found. A careful analysis of the circulation induced in water by the breaking process is carried out. It is seen that in the plunging regime the primary circulation induced by the breaking process scales with the velocity jump between the crest and the trough of the wave.The limits of the main assumptions of the numerical calculations are analysed. It is shown that up to half-wave period after the breaking onset, the Reynolds number of the simulation does not significantly affect the solution. In order to further support the findings, an estimate of the uncertainty of the numerical results is derived through several repetitions of the numerical simulation with small perturbations of the initial conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors present results of experimental and mathematical modelling of beach and dune erosion under storm events, which is based on a wave-by-wave modeling approach solving the wave energy equation for each individual wave.

Journal ArticleDOI
TL;DR: In this paper, a long and intermediate wave modeling package (COULWAVE) based on the non-linear Boussinesq equations are used to simulate the tsunami, including procedures to incorporate bottom friction, wave breaking, and overland flow during runup.

Journal ArticleDOI
TL;DR: In this paper, the authors observed the shoaling of three groups of nonlinear internal waves of depression over 35 km across the shelf, and the transition from depression to elevation waves is diagnosed by the integrated wave vorticity, which changes sign as the wave polarity changes sign.
Abstract: Observations off the New Jersey coast document the shoaling of three groups of nonlinear internal waves of depression over 35 km across the shelf. Each wave group experienced changing background conditions along its shoreward transit. Despite different wave environments, a clear pattern emerges. Nearly symmetric waves propagating into shallow water develop an asymmetric shape; in the wave reference frame, the leading edge accelerates causing the front face to broaden while the trailing face remains steep. This trend continues until the front edge and face of the leading depression wave become unidentifiable and a near-bottom elevation wave emerges, formed from the trailing face of the initial depression wave and the leading face of the following wave. The transition from depression to elevation waves is diagnosed by the integrated wave vorticity, which changes sign as the wave’s polarity changes sign. This transition is predicted by the sign change of the coefficient of the nonlinear term in the KdV equation, when evaluated using observed profiles of stratification and velocity.

Journal ArticleDOI
TL;DR: In this article, the effects of vertical resolution, different vertical mixing parameterization and surface roughness values on turbulent kinetic energy (k ) injection from breaking waves were assessed, and the model was applied to a realistic situation in the Adriatic Sea driven by numerical meteorological forcings and river discharges.

Journal ArticleDOI
TL;DR: In this article, sufficient conditions for wave breaking were found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale, which holds both on an infinite line and in a periodic domain.
Abstract: Sufficient conditions for wave breaking are found for the short- pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quan- tities of the short-pulse equation and holds both on an infinite line and in a periodic domain. Numerical illustrations of the finite-time wave breaking are given in a periodic domain.

Journal ArticleDOI
TL;DR: In this article, a numerical wave load model based on the incompressible Reynolds averaged Navier-Stokes equations and k-e equations has been used to investigate dynamic wave forces exerted on the bridge deck.
Abstract: Bridge decks in Escambia Bay were damaged during the storm surge of Hurricane Ivan in 2004. In this study, a numerical wave-load model based on the incompressible Reynolds averaged Navier–Stokes equations and k-e equations has been used to investigate dynamic wave forces exerted on the bridge deck. The volume of fluid method is adopted in the model to describe dynamic free surface, which is capable of simulating complex discontinuous free surface during wave breaking and wave-deck interactions. The model was satisfactorily tested against experimental data of uplift wave forces on horizontal plates. The validated model was applied to investigate wave forces acting on the bridge deck in Escambia Bay in the case of Hurricane Ivan. The time history of wave profiles, turbulent velocity fields, and dynamic uplift and horizontal forces acting on the full-scale bridge deck were simulated and analyzed. Results indicate that, during the storm surge event of Hurricane Ivan, the maximum uplifting wave forces were lar...

Journal ArticleDOI
TL;DR: In this paper, the authors study singular solutions of the problem of traveling gravity water waves on flows with vorticity and show that a sequence of regular waves converges to an extreme wave with stagnation points at its crests.