scispace - formally typeset
Search or ask a question

Showing papers on "Breaking wave published in 1999"


Journal ArticleDOI
TL;DR: In this article, a third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated.
Abstract: A third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third-generation wave models, the processes of wind generation, whitecapping, quadruplet wave-wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave-wave interactions and depth-induced wave breaking are added. In contrast to other third-generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

3,625 citations


Journal ArticleDOI
TL;DR: In this article, a third-generation spectral wave model for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases.
Abstract: A third-generation spectral wave model (Simulating Waves Nearshore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. These verification cases represent an increasing complexity in two- dimensional bathymetry and added presence of currents. In the most complex of these cases, the waves propagate through a tidal gap between two barrier islands into a bathymetry of channels and shoals with tidal currents where the waves are regenerated by a local wind. The wave fields were highly variable with up to 3 orders of magnitude difference in energy scale in individual cases. The model accounts for shoaling, refraction, generation by wind, whitecapping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. The effect of alternative formulations of these processes is shown. In all cases a relatively large number of wave observations is available, including observations of wave directions. The average rms error in the computed significant wave height and mean wave period is 0.30 m and 0.7 s, respectively, which is 10% of the incident values for both.

1,082 citations


Journal ArticleDOI
TL;DR: In this paper, a method for generating waves in Boussinesq-type wave models is described, which employs a source term added to the governing equations, either in the form of a mass source in the continuity equation or an applied pressure forcing in the momentum equations.

285 citations


Journal ArticleDOI
19 Nov 1999-Science
TL;DR: Temperatures acquired by the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) during shuttle mission STS-66 have provided measurements of stratospheric mountain waves from space, demonstrating that satellites can provide the global data needed to improve mountain wave parameterizations and hence global climate and forecast models.
Abstract: Temperatures acquired by the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) during shuttle mission STS-66 have provided measurements of stratospheric mountain waves from space. Large-amplitude, long-wavelength mountain waves at heights of 15 to 30 kilometers above the southern Andes Mountains were observed and characterized, with vigorous wave breaking inferred above 30 kilometers. Mountain waves also occurred throughout the stratosphere (15 to 45 kilometers) over a broad mountainous region of central Eurasia. The global distribution of mountain wave activity accords well with predictions from a mountain wave model. The findings demonstrate that satellites can provide the global data needed to improve mountain wave parameterizations and hence global climate and forecast models.

280 citations


Journal ArticleDOI
TL;DR: In this paper, a new method is developed to generate specific wave trains by using designed mass source functions for the equation of mass conservation, i.e., ∂ui∂xi = f(x, t), in the internal flow region.
Abstract: The flow motion of incompressible fluid can be described by Navier-Stokes equations with the continuity equation, which requires zero divergence of the velocity vector (i.e., ∂ui/∂xi = 0). A new method is developed to generate specific wave trains by using designed mass source functions for the equation of mass conservation, i.e., ∂ui∂xi = f(x, t), in the internal flow region. The new method removes the difficulty in specifying incident waves through an inflow boundary with the presence of strong wave reflection. Instead, only the open (radiation) boundary condition is needed in the simulation. By using different source functions, the writers are able to generate various wave trains, including the linear monochromatic wave, irregular wave, Stokes wave, solitary wave, and cnoidal wave. By comparing numerical results with analytical solutions, the writers have shown that the proposed method can accurately generate not only small amplitude waves but also nonlinear waves in both intermediate and shallow water...

273 citations


Journal ArticleDOI
TL;DR: In this paper, the shoaling and breaking of an internal solitary wave of depression on a uniform slope were studied experimentally, where the waves were generated with as large an amplitude as possible while minimizing mixing at the generation site, thus maximizing the amount of energy propagating onto the slope in the experiment.
Abstract: The shoaling and breaking of an internal solitary wave of depression on a uniform slope were studied experimentally. The waves were generated with as large an amplitude as possible while minimizing mixing at the generation site, thus maximizing the amount of energy propagating onto the slope in the experiment. Various bottom slopes, fluid layer thickness ratios, and density ratios were investigated. The mechanism leading to breaking was examined with flow visualization and particle image velocimetry. Since the layer thickness ratio primarily controls the length (LW) of the solitary wave (for a given amplitude a), it is found that the ratio of LW and the characteristic length of the slope LS determines the amount of energy reflected from the slope. The mixing efficiency of the breaking event, defined as the ratio of the increase of potential energy divided by the amount of wave energy lost at the slope, peaks at a maximum of 25% when LW/LS = 0.5, with a decrease in efficiency for points on either side of this peak value.

228 citations


Journal ArticleDOI
TL;DR: In this paper, a spectral parameterization of mean-flow forcing due to breaking gravity waves is described for application in the equations of motion in atmospheric models, based on linear theory and adheres closely to fundamental principles of conservation of wave action flux, linear stability, and wave-mean-flow interaction.
Abstract: A spectral parameterization of mean-flow forcing due to breaking gravity waves is described for application in the equations of motion in atmospheric models. The parameterization is based on linear theory and adheres closely to fundamental principles of conservation of wave action flux, linear stability, and wave‐mean-flow interaction. Because the details of wave breakdown and nonlinear interactions are known to be very complex and are still poorly understood, only the simplest possible assumption is made: that the momentum fluxes carried by the waves are deposited locally and entirely at the altitude of linear wave breaking. This simple assumption allows a straightforward mapping of the momentum flux spectrum, input at a specified source altitude, into vertical profiles of mean-flow force. A coefficient of eddy diffusion can also be estimated. The parameterization can be used with any desired input spectrum of momentum flux. The results are sensitive to the details of this spectrum and also realistically sensitive to the background vertical shear and stability profiles. These sensitivities make the parameterization ideally suited for studying both the effects of gravity waves from unique sources like topography and convection as well as generalized broad input spectra. Existing constraints on input parameters are also summarized from the available observations. With these constraints, the parameterization generates realistic variations in gravity-wave-driven, mean-flow forcing.

223 citations


Journal ArticleDOI
TL;DR: In this paper, numerical simulations of plunging breakers including the splash-up phenomenon are presented, where the motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation.
Abstract: Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than 80% of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.

200 citations


Journal ArticleDOI
TL;DR: In this paper, a time domain numerical model based on the fully nonlinear extended Boussinesq equations was used to investigate surface wave transformation and breaking-induced nearshore circulation.
Abstract: In this study, we use a time domain numerical model based on the fully nonlinear extended Boussinesq equations [Wei et al., 1995] to investigate surface wave transformation and breaking-induced nearshore circulation. The energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave run-up on the beach is simulated using a moving shoreline technique. We employ quasi fourth-order finite difference schemes to solve the governing equations. Satisfactory agreement is found between the numerical results and the laboratory measurements of Haller et al. [1997], including wave height, mean water level, and longshore and cross-shore velocity components. The model results reveal the temporal and spatial variability of the wave-induced nearshore circulation, and the instability of the rip current in agreement with the physical experiment. Insights into the vorticity associated with the rip current and wave diffraction by underlying vortices are obtained.

195 citations


Journal ArticleDOI
TL;DR: In this article, a physical model of the short wind wave spectrum in the wavelength range from a few millimeters to a few meters is proposed, where the spectrum shape results from the solution of the energy spectral density balance equation.
Abstract: A physical model of the short wind wave spectrum in the wavelength range from a few millimeters to few meters is proposed. The spectrum shape results from the solution of the energy spectral density balance equation. Special attention is paid to the description of the capillary range of the short wave spectrum. It is assumed that in this range the spectrum shape is determined mainly by the mechanism of generation of parasitic capillaries. This is described as the cascade energy transfer from the gravity to the capillary waves. Thus the capillary wave spectrum results through the balance between generation of capillaries and their viscous dissipation. The short gravity wave spectrum results through the balance between wind input and dissipation due to wave breaking. A parameterization of wind input is obtained in part 1 of the present paper. To describe the dissipation due to wave breaking, the approach developed by Phillips [1985] is used. The spectral rate of energy dissipation is presented in the form of a power dependence of the ratio of the saturation spectrum to some threshold level. It is further shown that the threshold level depends on the drift current shift in the water viscous sublayer, which affects the energy losses by wave breaking. To obtain a short wave spectrum which is valid in the whole wavenumber domain, the capillary and the short gravity wave spectra are patched in the vicinity of the wavenumber corresponding to the minimum phase velocity. This short wave spectrum is incorporated into the wind over waves coupled model developed in part 1 of the present paper. The measured statistical properties of the sea surface related to the short waves, such as the spectral shape of omnidirectional and up-wind spectra, their wind speed dependence and angular spreading, and the wind speed dependence of integral mean square slope and skewness parameters, are well reproduced by the model. Also the model well reproduces the measured wind speed dependence of the drag coefficient and of the coupling parameter.

177 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the generation of nearshore currents due to obliquely incident breaking waves, damping effects due to bottom friction, and diffusion effects caused by lateral momentum mixing caused by turbulence and depth-varying current velocities.
Abstract: The time dependent nearshore circulation field during 3 days of the SUPERDUCK field experiment is simulated. We consider the generation of nearshore currents due to obliquely incident breaking waves, damping effects due to bottom friction, and diffusion effects due to lateral momentum mixing caused by turbulence and depth-varying current velocities. Because of uncertainties in the friction and lateral mixing coefficients, numerical simulations are carried out for a realistic range of values for these coefficients. The resulting shear instabilities of the longshore current exhibit unsteady longshore progressive vortices with timescales of O(100 s) and length scales of O(100 m) and longer. The time dependent flow involves the strengthening, weakening, and interaction of vortices. Vortex pairs are frequently shed offshore. During this process, locally strong offshore directed currents are generated. We find that a stronger mean current and faster and more energetic vortex structures result as the friction coefficient is decreased. However, the longshore length scales of the resulting flow structures are not altered significantly. An increase in the mixing coefficient causes relatively small variations in the propagation speeds. However, the resulting flow structures are less energetic with larger longshore length scales. Shear instabilities are found to induce significant horizontal momentum mixing in the surf zone and affect the cross-shore distribution of the mean longshore current. Mixing due to the presence of the instabilities is found to be dominant over mixing caused by more traditional mechanisms such as turbulence. For values of the free parameters that reproduce the propagation speed of the observed motions, the frequency range within which shear instabilities are observed as well as the mean longshore current profile are predicted well.

Journal ArticleDOI
TL;DR: In this article, a combined experimental and numerical effort to study solitary wave runup and rundown on beaches is presented, where a two-dimensional numerical model that solves both mean flow and turbulence is employed.
Abstract: This paper presents a combined experimental and numerical effort to study solitary wave runup and rundown on beaches. Both nonbreaking and breaking solitary waves are investigated. A two-dimensional numerical model that solves both mean flow and turbulence is employed in this study. For the nonbreaking solitary wave on a steep slope, numerical results of the present model are verified by experimental data and numerical results obtained from the boundary integral equation method model, in terms of both velocity distribution and free surface profiles. The characteristics of flow patterns during runup and rundown phases are discussed. The vertical variations of the horizontal velocity component are large at some instances, implying that the shallow water approximation may be inaccurate even for the nonbreaking wave runup and rundown. For the breaking solitary wave on a mild slope, numerical results of the present model are compared with experimental data for free surface displacements. The present model is found to be more accurate than the depth-averaged equations models. Using this numerical model, the mean velocity field and turbulence distribution under the breaking wave are discussed.

Journal ArticleDOI
TL;DR: High-frequency field measurements of intertidal water velocities and accelerations were conducted simultaneously with recordings of inshore wave height at four representative sites in the mid-intertidal zone of a rocky shore to provide an improved, high-resolution picture of the nature of flows typical of littoral environments and their relationship to wave height.

Journal ArticleDOI
TL;DR: In this article, a new optical instrument was deployed in the surf zone in a trial experiment to measure bubble size distributions and visualize air entrainment and bubble formation mechanisms within breaking surf.
Abstract: A new optical instrument was deployed in the surf zone in a trial experiment to measure bubble size distributions and visualize air entrainment and bubble formation mechanisms within breaking surf. Images of bubbles and the evolving air–water mixture inside and beneath breaking wave crests are presented. The images resolve features of the air–water mixture to length scales of hundreds of microns across a 3.7-cm field of view. Two qualitatively different large-scale air entrainment processes are observed. First, intrusions of air and water, thought to be created by jets penetrating the water’s surface, fragment into plumes of bubbles. Second, an air cavity trapped by the overturning wave crest is observed to disintegrate into bubbles. The timescale for the evolution from a compacted air–water mass to individual bubbles was on the order of 90 ms or less for both of these processes. In addition, small-scale air filaments hundreds of microns wide and millimeters long have been discovered beneath wave...

Journal ArticleDOI
TL;DR: In this article, a morphological stability analysis for a long straight coast with a longshore bar is carried out for a situation with oblique wave incidence and a wave-driven longshore current.

Journal ArticleDOI
TL;DR: In this paper, surface gravity waves shoaling between 8m water depth and the shoreline on a barred beach indicate that breaking results in an increase in the directional spread of wave energy, in contrast to the directional narrowing with decreasing depth predicted by refraction theory (Snell's law).
Abstract: Observations of surface gravity waves shoaling between 8-m water depth and the shoreline on a barred beach indicate that breaking results in an increase in the directional spread of wave energy, in contrast to the directional narrowing with decreasing depth predicted by refraction theory (Snell's law). During low-energy wave conditions, when breaking-induced wave energy losses over the instrumented transect are small, the observed mean propagation direction and spread about the mean both decrease with decreasing depth, consistent with the expected effects of refraction. Nonlinearity causes high-frequency components of the spectrum to become directionally aligned with the dominant incident waves. During high-energy wave conditions with significant wave breaking on the sand bar, the observed mean directions still decrease with decreasing depth. However, the observed directional spreads increase sharply (nominally a factor of 2 for values integrated over the swell-sea frequency range) between the outer edge of the surf zone and the crest of the sand bar, followed by a decrease toward the shoreline. Observations on a nonbarred beach also show directional broadening, with spreads increasing monotonically from the outer edge of the surf zone to a maximum value near the shoreline. Although the mechanism is not understood, these spatial patterns of directional broadening suggest that wave breaking causes significant scattering of incident wave energy into obliquely propagating components.

Journal ArticleDOI
TL;DR: In this paper, a scaling of the breaking frequency based on wind energy input is proposed, consistent with energy dissipation being determined primarily by the high frequency tail of the wave spectrum.
Abstract: Breaking of surface waves was monitored with conductivity measurements at wind speeds up to 18 m s−1. This method of wave breaking detection is well defined but excludes microbreakers and breaking of very short gravity waves. Observations in both fetch limited and open ocean conditions reveal that wind speed or wave age are insufficient to characterize breaking activity. A scaling of the breaking frequency based on wind energy input is proposed. This scaling collapses the authors’ diverse datasets, consistent with energy dissipation being determined primarily by the high frequency tail of the wave spectrum. Breaking waves with significant air entrainment were observed to have wavelengths between ∼0.1 of the dominant waves and that of the largest wind waves. The median value of the period of breaking waves is approximately half the period of the dominant waves and the mean height of breaking waves is ∼0.7 times the significant wave height. Less than 10% of observed breaking events resulted in deep...

Journal ArticleDOI
TL;DR: In this article, a simple theoretical model to determine the equilibrium profile shape under breaking and non-breaking waves is presented, where the seaward transport in the undertow is locally balanced by a net vertical sedimentation.

Journal ArticleDOI
TL;DR: In this paper, a monochromatic wave train with a wave height of 14.5 cm and a wavelength of 121 cm was generated in a water depth, h, of 20 cm.
Abstract: This paper reports a set of laboratory data for breaking waves in the water of intermediate depth. A monochromatic wave train with a wave height of 14.5 cm and a wavelength of 121 cm was generated in a water depth, h, of 20 cm. The wave train breaks consistently at a distance of about 2h from the wave generator. The instantaneous velocity fields under the breaking waves on a two-dimensional vertical plane were measured by using the particle image velocimetry (PIV) technique. By repeating the same experiments twenty times and performing the ensemble average, mean velocity, mean vorticity, turbulence intensity, and other flow properties such as the Reynolds stress and the mean strain rate were calculated. Outside the aerated region, where the density of air bubbles is high, the experimental data show that the mean vorticity was of the same order of magnitude as (C/h) (≈6 s−1) with C being the phase speed. The maximum turbulence intensity outside the aerated region was in the order of magnitude of 0.1 C (≈11 cm/s). The time-averaged (over one wave period) turbulence intensity under the wave trough level was one order of magnitude smaller, i.e., it was about 0.04 C (≈4.8 cm/s). Based the experimental data, the transport equation for turbulent kinetic energy was further examined. The turbulence dissipation rate and its time scale were also estimated. Under the trough level at the measurement section, which was about 3h downstream from the breaking point, the turbulence production, and dissipation were of the same order of magnitude, but not identical. The turbulence advection, production, and dissipation were equally important, while the turbulence diffusion was almost negligible.

Journal ArticleDOI
TL;DR: In this paper, the evolution of the airflow instantaneous structure over an unsteady breaking wave propagating in a group is measured in detail using the digital particle image velocimetry technique.
Abstract: The evolution of the airflow instantaneous structure over an unsteady breaking wave propagating in a group is measured in detail using the digital particle image velocimetry technique. It is found that the boundary-layer over a breaking wave, the steepest in the group, separates at a point close to the sharp crest and reattaches in the front slope of the following wave. During breaking, the evolution of the turbulent vorticity is essentially unsteady and the recirculation zone of the separated flow takes the form of a large well-organized vortex. Links between the wave-crest geometry and geometrical features of the separation bubble have been established.

Journal ArticleDOI
TL;DR: In this paper, the rotation of the elliptical eye in the context of barotropic dynamics at three levels were explored: linear waves on a Rankin vortex, nonlinear Kirchhoff vortex, and with a nonlinear spectral model.
Abstract: An elliptical eye that rotated cyclonically with a period of approximately 144 minutes in Typhoon Herb 1996 was documented. The elliptical region had a semimajor axis of 30 km and a semiminor axis of 20 km. Two complete periods of approximately 144 min were observed in the Doppler radar data. The rotation of the elliptical eye in the context of barotropic dynamics at three levels were explored: linear waves on a Rankin vortex, a nonlinear Kirchhoff vortex, and with a nonlinear spectral model. The linear wave theory involves the existence of both the high (potential) vorticity gradient near the eye edge and the cyclonic mean tangential flow in the typhoon. The propagation of (potential) vorticity waves in the cyclonic mean flow makes the elliptical eye rotate cyclonically. The rotation period is longer than the period of a parcel trajectory moving in the cyclonic mean flow around the circumference, because the vorticity wave propagates upwind. The nonlinear theory stems from the rotation of Kirchhoff’s vortex. Estimates of the eye rotation period from both linear and nonlinear theories agree with observations of the eye rotation period when the observed maximum wind from Herb is used. Nonlinear numerical computations suggest the importance of the interaction of neutral vorticity waves, which determine the shape and the rotation period of the eye. The calculations also support the rotation of the eye in approximately 144 min in the presence of axisymmetrization, vorticity redistribution, wave breaking, and vortex merging processes.

Journal ArticleDOI
TL;DR: In this paper, a pulse-to-pulse coherent acoustic Doppler profiler is used for the measurement of turbulence in the ocean, which is obtained by identifying and filtering out deep water gravity waves in Fourier space and inverting the result.
Abstract: This paper presents laboratory and field testing of a pulse-to-pulse coherent acoustic Doppler profiler for the measurement of turbulence in the ocean. In the laboratory, velocities and wavenumber spectra collected from Doppler and digital particle image velocimeter measurements compare very well. Turbulent velocities are obtained by identifying and filtering out deep water gravity waves in Fourier space and inverting the result. Spectra of the velocity profiles then reveal the presence of an inertial subrange in the turbulence generated by unsteady breaking waves. In the field, comparison of the profiler velocity records with a single-point current measurement is satisfactory. Again wavenumber spectra are directly measured and exhibit an approximate −5/3 slope. It is concluded that the instrument is capable of directly resolving the wavenumber spectral levels in the inertial subrange under breaking waves, and therefore is capable of measuring dissipation and other turbulence parameters in the up...

Journal ArticleDOI
01 Jan 1999-Tellus B
TL;DR: In this paper, a nonhydrostatic cloud-resolving numerical model is used to simulate a 2-dimensional squall line in a domain of width 2048 km and depth 90 km.
Abstract: The observed cold temperatures in the summer mesosphere are dynamically maintained primarily through upwelling induced in response to the action of a zonal drag force caused by the breaking of upward propagating gravity waves. Tropospheric convective storms are believed to be important sources of gravity waves in the summer mesosphere, but little is known about the characteristics of mesospheric gravity waves generated by convection. As a first attempt to model such waves a nonhydrostatic cloud-resolving numerical model is used to simulate a 2-dimensional squall line in a domain of width 2048 km and depth 90 km. The simulation produces a broad spectrum of convectively generated gravity waves. These propagate into the middle atmosphere, forming a fan-like pattern of waves with amplitudes increasing with height, and eventually reach breaking amplitudes in the mesosphere. The resultant mesospheric wave-breaking produces strong zonal forcing, which is eastward to the east of the storm center and westward to the west of the storm center. Breaking of upward propagating waves also generates high frequency downward propagating secondary waves of short horizontal wavelength, and long vertical wavelength. The secondary waves have only a small influence on the net vertical transfer of momentum, but produce a strong signature in perturbation vertical velocity, featuring alternating positive and negative interference with the primary upward propagating modes. DOI: 10.1034/j.1600-0889.1999.00005.x

Journal ArticleDOI
TL;DR: An algorithm for the solution of general isotropic nonlinear wave equations is presented, based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral space.
Abstract: An algorithm for the solution of general isotropic nonlinear wave equations is presented The algorithm is based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral space The remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure Solving the linear part of the wave operator exactly effectively eliminates the stiffness of the original problem, characterized by a wide range of temporal scales The algorithm is tested and applied to several problems of three-dimensional long surface waves: solitary wave propagation, interaction, diffraction, and the generation of waves by flow over slowly varying bottom topography Other potential applications include waves in rotating and stratified flows and wave interaction with more pronounced topographic features

Journal ArticleDOI
TL;DR: In this article, a three-dimensional large eddy simulation (LES) of wave breaking was carried out and the following characteristics of vorticity and velocity field after wave breaking were discussed on the basis of results of the LES: (1) generation and evolution of the widthwise (shore direction) velocity component; (2) transition from a two-dimensional velocity field to a 3D one after wave-breaking; (3) evolution process of large-scale eddies comprised by horizontal, vertical and helical eddies; and (4) a coherent eddy
Abstract: A three-dimensional large eddy simulation (LES) of wave breaking was carried out. A numerical method for LES is proposed in this paper. The following characteristics of vorticity and velocity field after wave breaking are discussed on the basis of results of the LES: (1) generation and evolution of the widthwise (shore direction) velocity component; (2) transition from a two-dimensional velocity field to a three-dimensional one after wave breaking; (3) evolution process of large-scale eddies comprised by horizontal, vertical and helical eddies; and (4) a coherent eddy structure involving a turbulent bottom and wall boundary layer.

Journal ArticleDOI
TL;DR: In this article, a Lagrangian numerical simulation of breaking waves is performed by the moving particle semi-implicit (MPS) method, in which the Navier-Stokes equation is discritized based on the interaction of pa...
Abstract: A Lagrangian numerical simulation of breaking waves is performed by the moving particle semi-implicit (MPS) method, in which the Navier-Stokes equation is discritized based on the interaction of pa...

Journal ArticleDOI
TL;DR: In this paper, a primitive equation numerical model is adopted to investigate the orographic influence on a drifting cyclone over an idealized topography similar to that of Taiwan, and the abrupt increase of surface vorticity and the contraction of cyclone scale on the lee side are explained by the generation of new potential vortivities (PV) due to wave breaking associated with the severe downslope wind and hydraulic jump.
Abstract: In this study, a primitive equation numerical model is adopted to investigate the orographic influence on a drifting cyclone over an idealized topography similar to that of Taiwan. For a cyclone propagating from the east and impinging on the central portion of the mountain, a northerly surface jet tends to form upstream of the mountain between the primary cyclone and the mountain due to blocking and channeling effects. Two pressure ridges and one trough are also produced. When the cyclone approaches the mountain, the low-level vorticity and low pressure centers decelerate and turn southward upstream of the mountain due to orographic blocking. At the same time, the upstream low-level vorticity is blocked by the mountain. The abrupt increase of surface vorticity and the contraction of cyclone scale on the lee side are explained by the generation of new potential vorticity (PV) due to wave breaking associated with the severe downslope wind and hydraulic jump. The generation of this new PV is evidenc...

Journal ArticleDOI
TL;DR: In this article, a grant from the NASA Atmospheric Chemistry Modeling and Analysis Program (ACMAP) was used to support the development of a model for atmospheric chemistry models and their analysis.
Abstract: Work on this paper was supported by a grant from the NASA Atmospheric Chemistry Modeling and Analysis Program.

Book
09 Sep 1999
TL;DR: In this article, a mathematical representation of the wave equation is presented and an example of rarefaction and shock wave examples are given for traffic at a red light and the viscosity method Rarefaction waves.
Abstract: Introduction: Introduction to waves A mathematical representation of waves Partial differential equation Traveling and standing waves: Traveling waves The Korteweg-de Vries equation The Sine-Gordon equation The wave equation D'Alembert's solution of the wave equation Vibrations of a semi-infinite string Characteristic lines of the wave equation Standing wave solutions of the wave equation Standing waves of a nonhomogeneous string Superposition of standing waves Fourier series and the wave equation Waves in conservation laws: Conservation laws Examples of conservation laws The method of characteristics Gradient catastrophes and breaking times Shock waves Shock wave example: Traffic at a red light Shock waves and the viscosity method Rarefaction waves An example with rarefaction and shock waves Nonunique solutions and the entropy condition Weak solutions of conservation laws Bibliography Index.

Journal ArticleDOI
TL;DR: In this paper, a computationally inexpensive spectral gravity wave parameterization scheme was proposed, whose predictions approximate those of a full three-dimensional (in spectral space) spectral model of atmospheric gravity waves.
Abstract: This paper reports first steps toward a computationally inexpensive spectral gravity wave parameterization scheme whose predictions approximate those of a full three-dimensional (in spectral space) spectral model of atmospheric gravity waves. A reduction to two dimensions, as proposed by Hines, requiring the neglect of Coriolis and non-hydrostatic effects, is explored on the basis of comparisons with a full three-dimensional power-spectral model that includes Coriolis and non-hydrostatic effects. The reduction tries to be more realistic in terms of spectral shapes, though simpler in terms of wave-breaking criteria. It works remarkably well in the absence of, but less well in the presence of, background shear. The reasons for the discrepancies are under investigation, as are the implications for two-dimensional schemes, including Hines’ as well as ours.