Showing papers on "Breaking wave published in 1995"

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

Abstract: Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.

Observation of undertow and turbulence in a laboratory surf zone

Abstract: Undertow and turbulence in the surf zone have been studied in a wave flume for a spilling breaker and a plunging breaker. Fluid velocities across a 1 on 35 sloped false bottom were measured using a fiber-optic laser-Doppler anemometer, and wave decay and set-up were measured using a capacitance wave gage. The characteristics of mean flow and turbulence in spilling versus plunging breakers were studied. The mean flow is the organized wave-induced flow defined as the phase average of the instantaneous velocity, while the turbulence is taken as the deviations from the phase average. It was found that under the plunging breaker turbulence levels are much higher and vertical variations of undertow and turbulence intensity are much smaller in comparison with the spilling breaker. It was also found that turbulent kinetic energy is transported seaward under the spilling breaker and landward under the plunging breaker by the mean flow. The study indicates that there are fundamental differences in the dynamics of turbulence between spilling and plunging breakers, which can be related to the processes of wave breaking and turbulence production. It is suggested that the types of beach profile produced by storm and swell waves may be the results of different relationships between mean flow and turbulence in these waves.

Modeling of Breaking and Nonbreaking Long-Wave Evolution and Runup Using VTCS-2

Abstract: We present a variable grid finite-differences approximation of the characteristic form of the shallow-water-wave equations without artificial viscosity or friction factors to model the propagation and runup of one-dimensional long waves, referred to as VTCS-2. We apply our method in the calculation of the evolution of breaking and nonbreaking waves on sloping beaches. We compare the computational results with analytical solutions, other numerical computations and with laboratory data for breaking and nonbreaking solitary waves. We find that the model describes the evolution and runup of nonbreaking waves very well, even when using a very small number of grid points per wavelength. Even though our method does not model the detailed surface profile of wave breaking well, it adequately predicts the runup of plunging solitary waves without ad-hoc assumptions about viscosity and friction. This appears to be a further manifestation of the well-documented but unexplained ability of the shallow water wave equatio...

X band microwave backscattering from ocean waves

Abstract: Backscattering experiments at microwave frequencies were conducted off the west coast of Scotland in the summer of 1991. Using a dual-polarization, eight-frequency, X band, coherent scatterometer mounted on the bow of a boat, we measured time-resolved backscattering from ocean waves at a range of grazing angles from 10° to 70°. From the grazing-angle-dependent signals and their Doppler spectra, we are able to differentiate Bragg scattering from non-Bragg scattering and resolve “peak separation” between the vertical and horizontal polarizations. We observe instances of “super” events, i.e., instances when the horizontal polarization return power equals or exceeds the vertical polarization power at particular frequencies. We find that “super” events occur not only at low grazing angles but at any grazing angle for upwind viewing directions and obtain statistics for such occurrences as a function of grazing angle. We study the coherence properties of scatterers and find strong evidence that at low grazing angles, lifetime-dominated, non-Bragg scattering contributes noticeably to returns of both polarizations, but is dominant in providing returns for the horizontal polarization. We examine “spiking” events and find that they can be related to, but need not be limited to, breaking wave events. By comparing the data of upwind runs with cross-wind and circle runs, we obtain wind direction dependence of Doppler spectra, which further assists in the identification of scattering mechanisms.

Wave-driven flow over shallow reefs

Abstract: Long-term (1 month) observations of waves and currents over a natural reef are presented which show a strong correlation between offshore rms incident wave height and cross-reef currents at subtidal frequencies. The energy spectrum of the cross-reef currents shows a significant peak at twice the semidiurnal tidal frequency, while the spectrum of sea surface elevation over the reef flat shows no corresponding peak. Furthermore, experimental results reported by Gourlay (1993) show setup over the reef occurs in the absence of a beach, and the cross-reef transport decreases with an increase in the sea surface slope across the reef flat due to an increase in setup at the top of the reef face. Analytic solutions for flow forced by wave breaking over an idealized reef explain the above features of cross-reef flows in the absence of a beach. Through the surf zone on the reef face the cross-reef gradient in the radiation stress due to wave breaking is partitioned between balancing an offshore pressure gradient associated with setup over the reef and forcing a mean flow across the reef. Over the reef flat, where the depth is constant, there is no forcing due to wave breaking and the flow is driven by a pressure gradient which results from the setup through the surf zone. The magnitude of the setup through the surf zone is such that the transport across the reef flat matches the transport through the surf zone which is forced by the gradient in the radiation stress. Solutions are presented for general reef geometry, defined by the reef width and slope of the seaward reef face, and incident wave forcing, defined by the depth at the breakpoint and the depth of water over the reef. As the depth over the reef goes to zero, the solutions converge to the plane beach solutions described by Longuet-Higgins and Stewart (1964), wave setup is maximized, and the cross-reef transport is zero. In other cases the relative magnitudes of the setup and the cross-reef transport depend on the geometry of the reef and the incident wave forcing.

Three‐dimensional instabilities of film flows

Abstract: Two‐dimensional (2‐D) interfacial waves on flowing films are unstable with respect to both two‐ and three‐dimensional instabilities. In this paper, several distinct three‐dimensional instabilities that occur in different regions of the parameter space defined by the Reynolds numberR and the frequency f of forced two‐dimensional waves are discussed in detail. (a) A synchronous 3‐D instability, in which spanwise deformations of adjacent wave fronts have the same transverse phase, appears over a wide range of frequency. These transverse modulations occur mainly along the troughs of the primary waves and eventually develop into sharp and nearly isolated depressions. The instability involves many higher harmonics of the fundamental 2‐D waves. (b) A 3‐D surbharmonic instability occurs for frequencies close to the neutral curve f c (R). In this case, the transverse modulations are out of phase for successive wave fronts, and herringbone patterns result. It is shown that this weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two‐dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3‐D instabilities is complex. However, sufficiently far downstream, large‐amplitude solitary waves absorb the smaller waves and become dominant.

Trapping and acceleration in nonlinear plasma waves

Abstract: The trapping and acceleration of a test electron in a nonlinear plasma wave is analyzed in one dimension using Hamiltonian dynamics. The plasma wave is described by a nonlinear, cold fluid model. The maximum energy gain and the minimum energy required for trapping of the test electron are determined. The separatrix is plotted for several values of plasma wave amplitude. In the large wave amplitude limit, the maximum energy of a trapped electron scales as 2γ2pE2z, where γp is the relativistic factor associated with plasma wave phase velocity and Ez is the electric field amplitude of the nonlinear plasma wave. This is in contrast to the well‐known results for a sinusoidal wave, in which the maximum energy scales as 4γ2pEz. As the nonlinear plasma wave approaches wavebreaking, the maximum energy is given by γmax→4γ3p−3γp, where γmax is the relativistic factor of the trapped electron.

Vertical evolution of gravity wave spectra and the parameterization of associated wave drag

Abstract: Extensions of Weinstock's theory of nonlinear gravity waves and a parameterization of the related momentum deposition are developed. Our approach, which combines aspects of Hines' Doppler spreading theory with Weinstock's theory of nonlinear wave diffusion, treats the low-frequency part of the gravity wave spectrum as an additional background flow for higher-frequency waves. This technique allows one to calculate frequency shifting and wave amplitude damping produced by the interaction with this additional background wind. For a nearly monochromatic spectrum the parameterization formulae for wave drag coincide with those of Lindzen. It is shown that two processes should be distinguished: wave breaking due to instabilities and saturation due to nonlinear diffusionlike processes. The criteria for wave breaking and wave saturation in terms of wave spectra are derived. For a saturated spectrum the power spectral density's (PSD) dependence S(m) = AN2/m3 is obtained, where m is the vertical wavenumber and N is the Brunt-Vaisala frequency. Unlike Weinstock's original formulation, our coefficient of proportionality A is a slowly varying function of m and mean wind. For vertical wavelengths ranging from 10 km to 100 m and for typical wind shears, A varies from one half to one ninth. Calculations of spectral evolution with height as well as related profiles of wave drag are shown. These results reproduce vertical wavenumber spectral tail slopes which vary near the −3 value reported by observations. An explanation of these variations is given.

Photochemical-dynamical modeling of the measured response of airglow to gravity waves: 1. Basic model for OH airglow

Abstract: A photochemical-dynamical model for the OH Meinel airglow is developed and used to study the fluctuations in OH emission due to atmospheric gravity waves propagating through the mesosphere. The linear response of the OH Meinel emission to gravity wave perturbations is calculated assuming realistic photochemistry and gravity wave dynamics satisfying Hines (1960) isothermal windless model. The current model differs from prior models in that it considers fluctuations in vibrationally excited hydroxyl populations [OH(ν)] instead of fluctuations in the production rate of OH(ν). Two types of correction terms to the latter class of models are found, one involving advection of excited-state populations by the gravity wave and one involving quenching of OH(ν) by collisions with perturber molecules. Effects of these additional terms are expressed in terms of the so-called Krassovsky ratio η, which relates relative fluctuations in the column intensity measured by a passive optical instrument to relative fluctuations in the ambient temperature. The extra wave advection term is found to be unimportant under typical conditions, but quenching is important and has two major effects: (1) It makes η a vibrational-level-dependent quantity, and (2) it can lower η by more than 50% depending on the wave period. A typical range for η over a reasonably chosen range of wave parameters was found to be from less than 1 up to 9. The measuring instrument was also explicitly considered in the model formulation. Instead of simply assuming that the instrument measured the brightness-weighted temperature, as is commonly done in gravity wave response models, two common instruments for determining temperature from passive column-integrated measurements were explicitly modeled. The instruments modeled consisted of (1) a moderate-resolution instrument, such as a Michelson interferometer, which infers the temperature from the ratio of two rotational lines in a vibrational band (the rotational temperature) and (2) a high-resolution instrument, such as a Fabry-Perot interferometer, which uses the Doppler width of a single line to infer the temperature (the Doppler temperature). For gravity waves with large phase velocity (large-scale waves), calculations by both of these methods are found to be generally in agreement with each other and with the brightness-weighted temperature. However, for gravity waves with small phase velocity (small-scale waves) the two realistic simulations can differ from simulations using the brightness-weighted temperature by as much as 35%. The effect of vertical standing waves is considered by modifying the Hines model to include a rigid ground boundary. It is found that the standing waves have a profound effect on the phase of the gravity wave response. Values of η generated from the model are compared with published ground-based OH Meinel measurements of a quasi-sinusoidal short-period gravity wave by Taylor et al. (1991) from Sacramento Peak, New Mexico, at 15° elevation, as well as with the Svalbard polar-night data of Viereck and Deehr (1989). The agreement was found to be reasonable in both amplitude and phase for standing waves.

On the Subtropical Edge of the Stratospheric Surf Zone

Abstract: The formation of a subtropical “transport barrier” in the wintertime stratosphere is investigated in the context of a high-resolution shallow-water model in which Rossby waves are topographically forced on a zonally symmetric basic state. Two sets of experiments are performed: in the first “adiabatic” set, no dissipation or forcing of the mean state is imposed; in the second set, the layer thickness is relaxed to an equilibrium state taken to be representative of middle stratospheric radiative equilibrium temperatures. It is found that in the adiabatic case only a very weak subtropical barrier forms for forcing amplitudes that generate realistically steep potential vorticity gradients at the edge of the polar vortex; the vigorous wave breaking in the surf zone generates secondary waves that spread and, in turn, break well into the summer hemisphere. In contrast, the inclusion of relaxation to a realistic thermal equilibrium leads to the formation of a subtropical region of steep PV gradients. The...

A modeling investigation of the breaking wave roller with application to cross‐shore currents

Abstract: A mathematical model is developed for the creation and evolution of the aerated region, or “roller,” that appears as a wave breaks and passes through the surf zone. The model, which calculates the roller's cross-sectional area, is based on a short-wave averaged energy balance. The vertically integrated energy flux is split between the turbulent motion in the roller and the underlying organized wave motion, and the dissipation of energy is assumed to take place in the shear layer that exists at the interface between the two flow regimes. Calibration of the roller model is done by numerically solving equations for the cross-shore balances of mass and momentum, with roller contributions included, and then optimizing predictions of depth-averaged cross-shore currents. The laboratory data of Hansen and Svendsen [1984] for setup and cross-shore currents, driven by regular waves breaking on a planar beach, are used to set the roller model's fitting coefficient. The model is then validated utilizing five additional laboratory data sets found in the literature. Results indicate that employing stream function theory in calculating integral properties for the organized wave motion (wave celerity, and mass, momentum, and energy fluxes) significantly improves agreement as compared to results generated using linear wave theory. Using the roller model and stream function theory, root-mean-square error for the mean current is typically 19%. The bed stress is found to play a negligible role in the cross-shore mean momentum balance, relative to the radiation stress, setup, roller momentum flux, and convective acceleration of the current.

Shear stresses and mean flow in shoaling and breaking waves

Abstract: We investigate the vertical, wave averaged distributions of shear stresses and Eulerian flow in normally incident, shoaling and breaking waves. It is found that shear stresses are solely due to wave amplitude variations, which can be caused by shoaling, boundary layer dissipation and/or breaking wave dissipation. The resulting shear stress and mean flow distributions for these cases are derived, and compared with earlier work. The attractive, now frequently used modelling choice of specifying a shear stress at the mean surface level is discussed in the context of the constituent equations and related boundary conditions and constraints. A derivation of the shear stress at the mean surface level is given both by using the momentum balance and energy balance equations, which is shown to lead to the same result, if the effects of a changing roller are incorporated correctly). Finally, matching solutions for the shoaling and breaking wave cases between the boundary layer and the middle layer for the shear stresses and the wave averaged flow are derived.

An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM

Abstract: An efficient 2D non-linear numerical wave tank called LONGTANK has been developed based on a multi-subdomain (MSD) approach combined with the conventional boundary element method (BEM). The multi-subdomain approach aims at optimized matrix diagonalization, thus minimizing the computing time and reserved storage. The CPU per time step in LONGTANK simulation is found to increase only linearly with the number of surface nodes, which makes LONGTANK highly efficient especially when simulating long-time wave evolutions in space. Appropriate treatment of special points on the boundary ensures high resolution in LONGTANK simulation beyond initial deformation and breaking, which allows detailed study of breaking criterion, breaker morphology, breaking dissipation, vorticity generation, etc. Detailed numerical implementation has been given with demonstration of LONGTANK simulations.

Evolution of a quasi-steady breaking wave

Abstract: The stages of evolution of a quasi-steady breaker from the onset of a capillary pattern to a fully evolved breaking wave are characterized using high-image-density particle image velocimetry, which provides instantaneous representations of the free surface and the patterns of vorticity beneath it. The initial stage, which sets in at a low value of Froude number, involves a capillary pattern along each trough-crest surface of a quasi-stationary wave. The successive crests of the capillary pattern exhibit increasing scale and culminate in a single largest-scale crest of the free surface. Immediately upstream of the large-scale crest, the capillary pattern shows counterclockwise concentrations of vorticity at its troughs and regions of clockwise vorticity beneath its crests. The onset of the final, largest-scale crest exhibits two basic forms : one involving no flow separation; and the other exhibiting a small-scale separated mixing layer. At an intermediate value of Froude number, a breaker occurs and the capillary pattern is replaced by large-scale distortions of the free surface. The onset of separation, which involves flow deceleration along a region of the free surface having a large radius of curvature, leads to formation of a long mixing layer, which has substantial levels of vorticity. Downstream of this breaker, the long-wavelength wave pattern is suppressed. At the largest value of Froude number, the onset of flow separation rapidly occurs in conjunction with an abrupt change in slope of the surface, giving rise to vorticity concentrations in the mixing layer.

Breaking waves on beaches

Abstract: A comprehensive experimental study has been carried out to measure the velocity field of waves breaking on two types of beach. The measurement technique of Particle Image Velocimetry (PIV) has been used throughout to measure the fullfield, instantaneous velocity distributions. This technique is described in some detail with particular attention paid to the errors inherent when using PIV in this application. The first type of beach studied has a mild slope, typical of sandy beaches. PIV measurements have been carried out on 1:30 and 1:100 plane sloping beaches with monochromatic waves. The measured internal kinematics are compared to those predicted by the Boussinesqand Serre-type wave models, with some good agreement. However, there are some significant differences in the nearsurface region of the wave crest which tend to increase as the waves propagate up the beach. In addition to these theoretical comparisons, the Integral Properties of the waves on the 1:30 slope are calculated from the PIV measurements. The second type of beach examined is typical of a shingle beach. In addition to being steeper than the previous case, these beaches are also profiled, representing the shape of the beach formed under storm conditions. Two profiles have been modelled and three different monochromatic waves have been measured on each. The wave breaking processes are described and velocity measurements from each wave on both beaches are shown. Furthermore, a near-bed velocity comparison between the three waves at various positions along each beach has also been carried out in order to explain any potential on-shore and off-shore sediment motion.

Flow Characteristics of Undular Hydraulic Jumps. Comparison with Near-Critical Flows

Abstract: In open channels, the transition from supercritical to subcritical flows is called a hydraulic jump. For low upstream Froude numbers, free-surface undulations develop downstream of the jump. Such a hydraulic jump is called an undular jump. An earlier report (CHANSON 1993) described over 75 experiments on undular hydraulic jumps, performed in a rectangular channel in which the upstream flows were fully developed turbulent shear flows (both in terms of bottom and sidewall boundary layers). Visual and photographic observations indicated five types of undular jumps. One of the main flow characteristics was the presence of lateral shock waves for Froude numbers larger than 1.2. The present document describes a second series of more than 20 new experiments. The experiments were performed in the same flume previously used. The basic features of all the experiments are : a rectangular channel cross-section, and the upstream flows were uniform turbulent flows with fully-developed bottom and sidewall boundary layers. The experimental data include free-surface profiles, velocity distributions, pressure distributions and local head profiles upstream and downstream of undular jumps. The measurements were taken along the jump as well as across the flume width. The results show a major three-dimensional flow redistribution immediately upstream of the first wave crest. Velocity and pressure distributions were recorded at very close intervals in that region. And they provide some understanding of the flow redistribution mechanisms. The analysis of all the data (first and second series of experiments) shows that the energy dissipation occurs by the propagation of a train of stationary waves, lateral shock waves and a breaking wave (roller) mechanism at the first wave crest. The disappearance of the undular jump occurs for Froude numbers ranging from 1.5 to 2.9 and it is a function of the aspect ratio dc/W. Further the flow field properties (pressure, velocity, free-surface height) are functions not only of the upstream Froude number but also of the inflow conditions, the aspect ratio and the sidewall roughness. The flow characteristics of undular hydraulic jumps are compared also with near-critical flows : undular surges, free-surface undulations above broad-crested weirs, undulations downstream of backward-facing steps. After an introduction, the reader will find a bibliographic review on undular hydraulic jumps. Then the experimental apparatus is described. The experimental results are presented in two parts : the free-surface characteristics and the flow field characteristics. Later an analogy with near-critical flows is developed. At the beginning of the report, a table of contents, a list of symbols and a glossary can be found. At the end of the report, the appendices include : 1- a list of constants and fluid properties (App. A), 2- a table of unit conversions (App. B), 3- the experimental data of free-surface flow parameters (App. C, D, E) and 4- the data of pressure, velocity and total head distributions (App. F). A summary of the experiments is presented in appendix G. The experimental data of DARCY and BAZIN (1865), published in French, are given in appendix H.

Breaking of standing internal gravity waves through two-dimensional instabilities

Abstract: The evolution of an internal gravity wave is investigated by direct numerical computations. We consider the case of a standing wave confined in a bounded (square) domain, a case which can be directly compared with laboratory experiments. A pseudo-spectral method with symmetries is used. We are interested in the inertial dynamics occurring in the limit of large Reynolds numbers, so a fairly high spatial resolution is used (1292 or 2572), but the computations are limited to a two-dimensional vertical plane. We observe that breaking eventually occurs, whatever the wave amplitude: the energy begins to decrease after a given time because of irreversible transfers of energy towards the dissipative scales. The life time of the coherent wave, before energy dissipation, is found to be proportional to the inverse of the amplitude squared, and we explain this law by a simple theoretical model. The wave breaking itself is preceded by a slow transfer of energy to secondary waves by a mechanism of resonant interactions, and we compare the results with the classical theory of this phenomenon: good agreement is obtained for moderate amplitudes. The nature of the events leading to wave breaking depends on the wave frequency (i.e. on the direction of the wave vector); most of the analysis is restricted to the case of fairly high frequencies. The maximum growth rate of the inviscid wave instability occurs in the limit of high wavenumbers. We observe that a well-organized secondary plane wave packet is excited. Its frequency is half the frequency of the primary wave, corresponding to an excitation by a parametric instability. The mechanism of selection of this remarkable structure, in the limit of small viscosities, is discussed. Once this secondary wave packet has reached a high amplitude, density overturning occurs, as well as unstable shear layers, leading to a rapid transfer of energy towards dissipative scales. Therefore the condition of strong wave steepness leading to wave breaking is locally attained by the development of a single small-scale parametric instability, rather than a cascade of wave interactions. This fact may be important for modelling the dynamics of an internal wave field.

Surf-Zone Hydrodynamics

Abstract: Review paper on the recent progress in the field of wave modelling in the surf zone. The authors have the following concluding remarks (taken directly from the rapport): Wave breaking provides the forcing for larger scale motions in the surf zone. It is therefore probably both somewhat ironic as well as unfortunate that at the present time there exists no satisfactory theory to describe breaking and broken waves in the surf zone. This is currently a topic of intense research interest and we are confident that substantial progress will be made in the near future. While our overall understanding of wave-induced nearshore circulations seems to be fairly sound, there are a number of phenomena that clearly require further study. These include, but are not limited to, quantitatively accurate predictions of rip currents; the predictions of longshore currents on barred beaches; and the importance of alongshore inhomogenieties on nearshore circulations. Once again, these topics are currently being pursued by a number of investigators, and we expect considerable progress in the near future. Recent work has demonstrated that the surf zone is an important region for the generation of infragravity motions. While the present indications are that a substantial fraction of the infragravity energy seems to be generated in and near the surf zone, the existing models of surf zone generation of infragravity motions have not been verified. Shear waves seem to be amenable to an interpretation as a manifestation of an instability of the longshore current. Ongoing work on the nonlinear development of the instability and the importance of wave group forcing on these motions promises to yield interesting results. In conclusion, the subject of surf zone hydrodynamics is at an exciting stage of development right now and we expect that many of the issues will be clarified in the near future. We may also expect that the ongoing and future work will discover phenomena which we are currently unaware of.

Correlations between Ambient Noise and the Ocean Surface Wave Field

Abstract: Measurements of the ambient noise spectrum level N with simultaneous, coincident wind and wave measurements were made from RP FLIP in fall 1991. The measurements were designed to investigate the correlation between the ambient noise and relevant surface wave parameters. The results suggest that wave parameters related to the incidence of wave breaking correlated well with the ambient noise level. The correlation between N and the rms wave amplitude a was found to he poor but that between N and the rms amplitude of the local wind sea aw was comparable to that between wind speed U and N. Similar good correlations were found between the rms wave slope s and N, and the higher frequency surface wave spectral levels and N. Correlations between the surface wave dissipation estimates D based on the Hasselmann and Phillips models and the ambient noise were comparable to those between the wind speed and the ambient noise. The mean square acoustic pressure was found to be proportional to Dn with n in the ra...

A spectral model for waves in the near shore zone

Abstract: The present paper describes the second phase in the development of a fully spectral wave model for the near shore zone (SWAN). Third-generation formulations of wave generation by wind, dissipation due to whitecapping and quadruplet wave-wave interactions are added to the processes of (refractive) propagation, bottom friction and depth-induced wave breaking that were implemented in the first phase (Holthuijsen et al., 1993). The performance and the behaviour of the SWAN model are shown in two observed cases in which waves are regenerated by the wind after a considerable decrease due to shallow water effects. In the case of the Haringvliet (a closed branch of the Rhine estuary, the Netherlands) reasonable results in terms of significant wave heights were obtained. In the case of Saginaw Bay (Lake Huron, USA), the SWAN model underestimates the significant wave height deep inside the bay (as did two other models). Due to the absence of triad wave-wave interactions in the model the mean period is not properly shifted to the higher frequencies in shallow water. Adding these triads is planned for the next phase of developing the SWAN model.

Numerical simulation and validation of plunging breakers using a 2d navier-stokes model

Abstract: The numerical model SKYLLA, developed for simulation of breaking waves on coastal structures is described. The model is based on the Volume Of Fluid method and solves the two-dimensional (2DV) Navier-Stokes equations. Weakly reflecting boundary conditions allow waves to enter and leave the computational domain. Impermeable boundaries can be introduced to simulate a structure. A two-model approach can be used to simulate overtopping over a low crested structure. Results obtained with the model are compared with those obtained with physical model tests for waves on a 1:20 slope of a submerged structure.

Model for decay of random waves in surf zone

Abstract: A model for the decay of random waves in the surf zone that requires transformation of only one representative wave height [root-mean square (RMS)] without making any assumption about the shape of the probability-density function is presented. The breaker decay model proposed by Dally is used as a starting point in the derivation of the new model. It is assumed that random wave properties in the surf zone may be obtained by individually transforming a large number of waves across shore and adding together the effect from each single-wave component. In deeper water, outside the surf zone, where wave breaking is negligible, a Rayleigh distribution is employed to characterize the randomness of the sea. This semianalytic model is compared with a complete Monte Carlo–simulation approach for different beach profile shapes, including barred profiles, and macrofeatures of wave height and energy flux transformation across the surf zone are similar for the two approaches. Comparisons are made in the paper with labo...