Showing papers on "Breaking wave published in 1990"
30 Jun 1990-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, a detailed velocity survey of the breaking region was made and ensemble averages taken of the non-stationary flow was taken to investigate the influence of breaking on the evolution of the wave field.
Abstract: The results of laboratory experiments on unsteady deep-water breaking waves are reported. The experiments exploit the dispersion of deep-water waves to generate a single breaking wave group. The direct effects of breaking are then confined to a finite region in the wave channel and the influence of breaking on the evolution of the wave field can be examined by measuring fluxes into and out of the breaking region. This technique was used by us in a preliminary series of measurements. The loss of excess momentum flux and energy flux from the wave group was measured and found to range from 10% for single spilling events to as much as 25% for plunging breakers. Mixing due to breaking was studied by photographing the evolution of a dye patch as it was mixed into the water column. It was found that the maximum depth of the dye cloud grew linearly in time for one to two wave periods, and then followed a t$^{\frac{1}{4}}$ power law (t is the time from breaking) over a range of breaking intensities and scales. The dyed region reached depths of two to three wave heights and horizontal lengths of approximately one wavelength within five wave periods of breaking. A detailed velocity survey of the breaking region was made and ensemble averages taken of the non-stationary flow. Mean surface currents in the range 0.02-0.03 C (C is the characteristic phase speed) were generated and took as many as 60 wave periods to decay to 0.005 C. A deeper return flow due to momentum lost from the forced long wave was measured. Together these flows gave a rotational region of approximately one wavelength. Turbulent root mean square velocities of approximately 0.02 C were measured near the surface and were still significant at depths of three to four wave heights. More than 90% of the energy lost from the waves was dissipated within four wave periods. Subsequently measured kinetic energy in the residual flow was found to have a t$^{-1}$ dependence. Correlation of all the above measurements with the amplitude, bandwidth and phase of the wave group was found to be good, as was scaling of the results with the centre frequency of the group. Local measures of the breaking wave were not found to correlate well with the dynamical measurements.
571 citations
01 Sep 1990
TL;DR: A new method for animating water based on a simple, rapid and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations, which can generate the effects of wave refraction with depth.
Abstract: We present a new method for animating water based on a simple, rapid and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations. The approximation gives rise to a version of the wave equation on a height-field where the wave velocity is proportional to the square root of the depth of the water. The resulting wave equation is then solved with an alternating-direction implicit method on a uniform finite-difference grid. The computational work required for an iteration consists mainly of solving a simple tridiagonal linear system for each row and column of the height field. A single iteration per frame suffices in most cases for convincing animation.Like previous computer-graphics models of wave motion, the new method can generate the effects of wave refraction with depth. Unlike previous models, it also handles wave reflections, net transport of water and boundary conditions with changing topology. As a consequence, the model is suitable for animating phenomena such as flowing rivers, raindrops hitting surfaces and waves in a fish tank as well as the classic phenomenon of waves lapping on a beach. The height-field representation prevents it from easily simulating phenomena such as breaking waves, except perhaps in combination with particle-based fluid models. The water is rendered using a form of caustic shading which simulates the refraction of illuminating rays at the water surface. A wetness map is also used to compute the wetting and drying of sand as the water passes over it.
430 citations
TL;DR: In this article, the spectrum of gravity wave at each height is calculated directly from the wave equation and wave dissipation is approximately accounted for by a diffusion term, assuming that many wave dissipations can be approximately described by a scale-dependent diffusion process.
Abstract: For a highly idealized condition, the spectrum of saturated and unsaturated gravity waves at each height is calculated directly from the wave equation. A principal feature of this wave equation is the inclusion of wave dissipation, although in an approximate form. In the absence of wave absorption, reflection, radiation, wind shears, resonant wave–wave interactions and other sources and sinks, this dissipation at each height is determined solely by the “turbulent” or chaotic state caused by off-resonant wave–wave interactions and instability of the (broad) wave spectrum at that height. The dissipation is approximately accounted for by a diffusion term. The appropriate diffusivity is self-consistent with the continuum of spectral waves that cause the chaotic state and is argued to be scale dependent. An inverse calculation is also made of what the observed spectra imply for wave dissipation—again assuming that many wave dissipations can be approximately described by a scale-dependent diffusion pro...
146 citations
TL;DR: In this paper, a detailed physical model of the life history of a typical bubble plume, from its formation by a breaking wave to its dissipation into the background bubble population, is given, and the relationship between the early, acoustically relevant stages in bubble-plume development and the associated, remotely detectable whitecap is described.
Abstract: A detailed physical model of the life history of a typical bubble plume, from its formation by a breaking wave to its dissipation into the background bubble population, is given, and the relationship between the early, acoustically relevant stages in bubble-plume development and the associated, remotely detectable whitecap is described. The manner in which the fraction of the sea surface covered by stage A spilling crests and by stage B mature whitecaps depends upon wind speed and upon wind stress or friction velocity is investigated. Formal expressions are given whereby near-surface bubble concentrations can be estimated from observations of fractional whitecap coverage or from measurements of the 10-m elevation wind speed. >
144 citations
TL;DR: In this article, a more stable free surface representation based on quasi-spline elements and an improved corner solution combining the enforcement of compatibility relationships in the double-nodes with an adaptive integration was proposed.
Abstract: The numerical model for nonlinear wave propagation in the physical space, developed by Grilli, et al. 12,13 , uses a higher-order BEM for solving Laplace's equation, and a higher-order Taylor expansion for integrating in time the two nonlinear free surface boundary conditions. The corners of the fluid domain were modelled by double-nodes with imposition of potential continuity. Nonlinear wave generation, propagation and runup on slopes were successfully studied with this model. In some applications, however, the solution was found to be somewhat inaccurate in the corners and this sometimes led to wave instability after propagation in time. In this paper, global and local accuracy of the model are improved by using a more stable free surface representation based on quasi-spline elements and an improved corner solution combining the enforcement of compatibility relationships in the double-nodes with an adaptive integration which provides almost arbitrary accuracy in the BEM numerical integrations. These improvements of the model are systematically checked on simple examples with analytical solutions. Effects of accuracy of the numerical integrations, convergence with refined discretization, domain aspect ratio in relation with horizontal and vertical grid steps, are separately assessed. Global accuracy of the computations with the new corner solution is studied by solving nonlinear water wave flows in a two-dimensional numerical wavetank. The optimum relationship between space and time discretization in the model is derived from these computations and expressed as an optimum Courant number of ∼0.5. Applications with both exact constant shape waves (solitary waves) and overturning waves generated by a piston wavemaker are presented in detail.
141 citations
TL;DR: In this article, the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress are investigated.
Abstract: In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress. Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves. In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.
124 citations
TL;DR: In this paper, a general way of characterizing what is meant by the classical, dissipative type of wave-induced mean motion is to say that the waveinduced mean motions are balanced motions, in a sense to be discussed, and that the effective mean force corresponds to the potential vorticity transport that results from wave dissipation.
Abstract: Wave-mean interactions of the classical type, in which the effect of the waves on the mean motion depends on wave breaking or other types of wave dissipation, are to be sharply distinguished from other types of wave-mean interaction that have no such dependence on dissipation. Important cases arise both for unstratified (homentropic) flow and for stably stratified flow under gravity. A very general way of characterizing what is meant by the classical, dissipative type of wave-induced mean motion is to say that the wave-induced mean motions are balanced motions, in a sense to be discussed, and that the effective mean force corresponds to the wave-induced vorticity or potential vorticity transport that results from wave dissipation. For a stratified fluid, ‘potential vorticity’ is to be understood in the sense of Rossby and Ertel. ‘Balanced’ is to be understood in whatever sense is needed to imply the invertibility of the vorticity or potential vorticity field to give the other fields describing the mean motion. At first sight this appears to require that an appropriate Mach, Froude and/or Rossby number for the mean motion should be much smaller than unity, but the fundamental, and in practice less stringent, principal requirement appears to be that the spontaneous emission, or aerodynamic generation, of sound, gravity and/or inertio-gravity waves by the mean flow should be weak.Three basic examples of dissipative wave-induced mean flow generation are presented and discussed. The first is the transport of vorticity by dissipating sound waves, which gives rise to classical acoustic streaming of the quartz-wind type. The transport or flux of vorticity can always be taken to be an exactly antisymmetric tensor; and in the case of a plane sound wave this tensor fluctuates about a mean value equal to and E are the mean mass and wave-energy densities, ω the intrinsic frequency, and k the wavenumber. This is a succinct way of making evident why it is only the contribution q to the radiation stress convergence per unit mass that is significant for the generation of mean streaming. The second example is the transport of Rossby–Ertel potential vorticity (PV) by internal gravity waves that are either dissipating laminarly, or ‘breaking’ to produce inhomogeneous three-dimensional turbulence. This PV transport gives rise to mean streaming in much the same way as the vorticity transport in the acoustic example. The transport or flux of PV can always be taken to be directed exactly along the isentropic surfaces θ = constant of the stable stratification, where θ is potential temperature or potential density as appropriate; and in the case of a plane internal gravity wave the wave-induced PV transport fluctuates about a mean value G × q, where G is the basic gradient of θ associated with the stable stratification. This is a succinct way of making evident why it is only the projection of q onto the basic stratification surfaces that is significant. In both the acoustic and the internal-gravity examples the transport is non-advective, and often upgradient. The third example is the corresponding problem for Rossby waves, in which the typical effect of wave dissipation is a downgradient PV transport. This is brought about in an entirely different way, namely through advection of PV anomalies by the fluctuating velocity field of the wave motion, whether the dissipation be laminar or by breaking.Processes of the sort idealized in the second and third examples are ubiquitous in the Earth's atmosphere and, for instance, largely control the strength of the global-scale middle atmospheric circulation and hence, for instance, the e-folding residence times (∼ 102 y) of man-made chlorofluorocarbons in the lower atmosphere.
88 citations
Book•
01 May 1990
TL;DR: In this article, the authors present the second in a series on the numerical model SBEACH (Storm-induced BEAch CHange), which calculates dune and beach erosion produced by storm waves and water levels; bar formation and movement produced by breaking waves are also simulated.
Abstract: : This report is the second in a series on the numerical model SBEACH (Storm-induced BEAch CHange). SBEACH calculates dune and beach erosion produced by storm waves and water levels; bar formation and movement produced by breaking waves are also simulated. The model is empirically based and was originally developed from a large data set of net cross-shore sand transport rates and beach profile change observed in large tanks. The empirical formulation, model sensitivity tests, and a field validation case are described in Report 1. In the present report, Report 2, the capability of the model to simulate berm and dune erosion is evaluated using recently acquired field data from both US east and west coasts. Hypothetical storm events are also simulated to demonstrate model applicability and potential uses for predicting initial adjustment of beach fill and its response to storm action, including poststorm recovery. A complete description of the mathematical formulation of the model is provided with numerical algorithms comprising the solution scheme. Improvements of the model are also presented. The associated wave model has been generalized by using complete linear wave theory everywhere on the profile without shallow-water approximations, a capability important in general applications for irregular bottom profiles subjected to waves of widely ranging characteristics. Refraction has been included, and an option is provided to randomize the wave input for better representing forcing conditions in the field.
88 citations
TL;DR: In this paper, the authors investigated the effect of breaking internal gravity waves on the circulation in the middle atmosphere of Mars using a quasi-geostrophic delta-plane dynamical model of the zonal-mean flow.
Abstract: The possible effect of breaking internal gravity waves on the circulation in the middle atmosphere of Mars was investigated using a quasi-geostrophic delta-plane dynamical model of the zonal-mean flow. The results of model simulations show that breaking gravity waves of intermediate horizontal scales (100-1000 km wavelengths) could act to 'close off' the winter westerly circumpolar jet in the 40-80 km altitude region and induce strong high-latitude warming at these levels, in accordance with recent thermal measurements indicating that Martian winter polar latitudes may be very warm in this middle atmospheric region. It was also found that, below about 40 km, wave breaking does not induce much warming, consistent with available data showing that winter high altitudes are normally very cold at lower levels.
86 citations
TL;DR: In this article, the authors measured the impact pressure and resulting wall deflection from breaking oscillatory waves on a vertical wall with 1/10 foreshore slope and found that the longerlasting low impact forces are more effective in producing the larger wall deflections.
69 citations
TL;DR: In this paper, it was shown that the theoretical basis of this result is extremely sensitive to an ad hoc assumption about the nature of the wavelength at which wave energy is delivered to dissipation (turbulence), and the method used by Gregg (1989) to calculate instantaneous wave field energy level E is incorrect and will seriously underestimate E in cases where E is greater than EGM, the energy level of the GM (Garrett and Munk, 1975) canonical internal wave field, and the range of variation of E and buoyancy frequency N in the data sets reported by Gregg
Abstract: This paper questions a recent claim (Gregg, 1989) that a first-order understanding of the link between internal waves and turbulence has been achieved. It is demonstrated that (1) the theoretical basis of this result is extremely sensitive to an ad hoc assumption about the nature of the wavelength at which wave energy is delivered to dissipation (turbulence), (2) the method used by Gregg (1989) to calculate instantaneous wave field energy level E is incorrect and will seriously underestimate E in cases where E is greater than EGM, the energy level of the GM (Garrett and Munk, 1975) canonical internal wave field, and (3) the range of variation of E and buoyancy frequency N in the data sets reported by Gregg (1989) is not sufficient to rule out alternative scalings.
TL;DR: In this article, the observed characteristics of some basic integral parameters for regular waves essential for the determination of the energy flux, the radiation stress, and the energy dissipation throughout the surf zone are discussed.
TL;DR: Greenwood et al. as mentioned in this paper measured the horizontal, cross-shore velocity field in the lowermost meter of the water column, in association with measurements of waves and the mean elevation of water surface, across a nontidal, low relief, barred surf-zone.
TL;DR: In this paper, a closed-form transformation of random variable is performed to yield the probability density function for wave height across a beach of uniform slope starting from a Rayleigh distribution well seaward of the surf zone, the transformation is accomplished by using linear wave theory for shoaling and an analytical solution of a model for decay of regular waves due to breaking.
TL;DR: In this article, the influence of local wind on nearshore breaking waves was investigated in a laboratory wave-wind flume and the breaker location, geometry, and type were found to depend strongly upon the wind direction.
Abstract: The influence of local wind on nearshore breaking waves was investigated in a laboratory wave‐wind flume. The breaker location, geometry, and type were found to depend strongly upon the wind direction. Onshore winds cause waves to break earlier, to break in deeper water farther from shore, and to spill; offshore winds cause waves to break later, to break in shallower water closer to shore, and to plunge. For onshore winds, it was observed that breaking of the wind‐generated ripples can initiate spilling breaking of the primary underlying wave by providing a perturbation on the crest of the underlying wave as it shoals. The implications of these results are that surf zone width, currents, and sediment transport can be affected by local winds. Thus, engineering estimates of these quantities could be improved by consideration of local wind. Surf zone dynamics models that ignore wind or include wind only as a surface shear may be missing a very important effect of the wind—its effect on the initiation and mec...
TL;DR: In this article, a new investigation is made of internal wave generation by surface waves, which is put into a unified form that includes a model of surface wave damping, and it is shown that for wind speeds between 7 and 20 m s−1 the internal wave field loses about 10−4 W m−2 to the surface wave field.
Abstract: A new investigation is made of internal wave generation by surface waves. Previous theories are put into a unified form that includes a model of surface wave damping. Calculations using the complete theory, which do not seem to have been made previously, indicate that for wind speeds between 7 and 20 m s−1 the internal wave field loses about 10−4 W m−2 to the surface wave field. This would lead to a decay time of about 10 days for the high frequency portion of the internal wave field if an energy source were not available to maintain it. Possible sources for this energy are discussed. In contrast to this result for wind waves, a strong highly collimated ocean swell can lead to rapid growth of high frequency internal waves. The effects of nonlinear surface wave modulation and wave blocking are also discussed.
TL;DR: In this paper, the authors analyzed the physical mechanism that supports this pulsation and demonstrated that it is due to Kelvin-Helmholtz instability of the new (quasi-parallel) mean flow that is established in the lee of the obstacle by the wave, mean-flow interaction induced by wave breaking.
Abstract: Recently reported Doppler lidar observations of the downslope component of flow velocity made during the occurrence of a mountain windstorm at Boulder, Colorado, have established that such storms are characterized by an intense pulsation of windspeed with characteristic period(s) near 10 minutes. Scinocca and Peltier (1989) have independently shown such pulsations to be predicted on the basis of two-dimensional nonhydrostatic numerical simulations in which internal waves launched by stratified flow over smooth topography are forced to exceed critical steepness and, therefore, “break.” In the present paper we analyze the physical mechanism that supports this pulsation. As we demonstrate, it is due to Kelvin-Helmholtz instability of the new (quasi-parallel) mean flow that is established in the lee of the obstacle by the wave, mean-flow interaction induced by wave breaking. As such the pulsation represents a secondary instability of the stratified flow in which the primary instability is that associ...
TL;DR: In this article, the shape and phase speed of individual solitary waves were observed and compared with theoretical predictions, showing that individual wave characteristics (shape, amplitude and speed) were very nearly preserved after collision with another wave.
Abstract: Fluid of a lower density and viscosity can buoyantly rise through a viscous fluid through conduits that support simple pipe flows. The conduits also support solitary waves which exhibit near soliton behavior. Laboratory experiments on the characteristics of the solitary waves and their interactions have been conducted and compared with theory. The observations of shape and phase speed of individual waves show good agreement with the theoretical predictions. Large amplitude waves traveled slightly faster than the theoretical predictions. The discrepancy is probably due to higher order effects associated with wave slope not accounted for in the theory. Individual wave characteristics (shape, amplitude and speed) were very nearly preserved after collision with another wave. A phase jump of each wave was the main consequence of an interaction. The larger (faster) waves increased in amplitude by an average of 5 percent after collision and their phase speeds decreased by an average of 4 percent. The sm...
TL;DR: In this paper, the authors simulate the development of a moderately steep wavetrain, using evolution equations correct to fourth order in the wave steepness, with an added term simulating effects of wave breaking, finding that the breaking damps the developing sidebands selectively, such that the most unstable lower sideband comes out of the modulation-breaking process being the dominant one.
Abstract: We simulate the development of a moderately steep wavetrain, using evolution equations correct to fourth order in the wave steepness(see Dysthe (1979) and Lo and Mei (1985)), with an added term simulating effects of wave breaking. It is found that the breaking damps the developing sidebands selectively, such that the most unstable lower sideband comes out of the modulation-breaking process being the dominant one. The reason for this, in our opinion, is the tendency towards spatial localization of the part of the wavetrain contributing to the upper sidebands. This “high-frequency” part of the signal seems to concentrate around the steepest portions of the wavetrain, where breaking occurs. This is found both in our simulations and in experimental records (Melville 1983).
01 Jan 1990
TL;DR: In this paper, a numerical model is presented for predicting the now and armor response on a rough permeable slope as well as the flow in a permeable underlayer for a normally incident wave train.
Abstract: KOBAYASHI, N. and WURJANTO, A., 1990. Numerical model for waves on rough slopes. Jour nal of Coastal Research, SI#7, 149-166. Fort Lauderdale (Florida). ISSN 0749-0208. A numerical model is presented for predicting the now and armor response on a rough permeable slope as well as the flow in a permeable underlayer for a normally incident wave train. In addi tion to the continuity and momentum equations used to compute the flow field, an equation of energy is used to estimate the rate of energy dissipation due to wave breaking. Computation is made for six test runs to examine the accuracy and capability of the numerical model for sim ulating the fairly detailed hydrodynamics and armor response under the action of regular waves. The computed critical stability number for initiation of armor movement is compared with the measured stability number corresponding to the start of the damage under irregular wave action to quantify the limitations of the regular wave approximation. The computed wave run-up, run-down and reflection coefficients are shown to be in qualitative agreement with available empirical formulas based on regular wave tests. ADDITIONAL INDEX WORDS: Waves, reflection, run-up, armor units, breakwaters.
01 Jan 1990
TL;DR: The fluid dynamics of wave propagation, wave breaking, and the resulting turbulence poses three major challenges to research on middle atmospheric dynamics and chemical transport as mentioned in this paper, including the unjustifiability of the eddydiffusivity concept, under conditions often met with in the atmosphere, ill-understood nature of the Rossby-wave-associated dynamical feedbacks on the global circulation, and an acute difficulty in parameterizing vertical mixing by convectively overturning gravity waves in the mesosphere and lower thermosphere.
Abstract: The fluid dynamics of wave propagation, wave breaking, and the resulting turbulence — be it the fully three-dimensional small-scale turbulence due to breaking internal gravity waves, or the layerwise two-dimensional turbulence due to breaking Rossby waves — poses three major challenges to research on middle atmospheric dynamics and chemical transport. These are, first, the unjustifiability of the eddy-diffusivity concept, under conditions often met with in the atmosphere, second, the ill-understood nature of the Rossby-wave-associated dynamical feedbacks on the global circulation and, third, an acute difficulty in parameterizing vertical mixing by convectively overturning gravity waves in the mesosphere and lower thermosphere.
TL;DR: In this article, the authors describe the mechanism of sand suspension due to wave breaking on the basis of detailed laboratory measurements of suspended sand concentration near the breaking point with a light absorbing-type probe.
Abstract: This paper describes the mechanism of sand suspension due to wave breaking on the basis of detailed laboratory measurements of suspended sand concentration near the breaking point with a light-absorption-type probe. The distribution and the total amount of suspended sand were evaluated using the data obtained, which were carefully corrected for the contamination due to air bubbles entrained through wave breaking. A predictive formula for the amount of sand suspended by a breaker was proposed for a wide range of conditions.
TL;DR: In much of the practical parameter range, mathematical predictions for steady, progressive waves are available from a range of orders from Stokes, Cnoidal and Fourier theories as discussed by the authors.
Abstract: In much of the practice of coastal and ocean engineering, the question of which wave theory to use has been largely of academic interest. Consideration of shallow water and/or higher order wave theories has been complicated by the relative inaccessibility of these theories. The literature is extensive and frequently confusing, which has often led to the adoption of linear wave theory, whether or not it is appropriate. In much of the practical parameter range, mathematical predictions for steady, progressive waves are available from a range of orders from Stokes, Cnoidal and Fourier theories. The differences are often considerable.
TL;DR: In this paper, the stability of the propagation of bright and dark coupled solitary waves that may travel in the orthogonal polarization modes of a birefringent nonlinear optical fiber was investigated.
Abstract: We investigate the stability of the propagation of bright and dark coupled solitary waves that may travel in the orthogonal polarization modes of a birefringent nonlinear optical fiber In the anomalous dispersion regime, the coupled-solitary-wave decay is self-induced by modulational polarization instability of the dark component background pulse In the normal dispersion regime, stable propagation only occurs for distances of the order of one linear beat length We identify different instability mechanisms such as gray soliton formation, polarization wave breaking, polarization dispersion, and self-stimulated Raman scattering that leads to asymmetric coupled-solitary-wave breakup
TL;DR: In this paper, the Boundary Element Method (BEM) is applied to the computation of the interaction between highly nonlinear solitary waves and a plane steep and gentle slopes, and the results show that the BEM used here is capable of accurately describing the wave flow and interaction with a plane slope (2.88° to 90°), in great detail.
Abstract: An efficient Boundary Element Method (BEM) solving fully nonlinear waterwave problems in the physical space has been developed in our earlier papers. Its detailed numerical features have been presented elsewhere. In the present paper, this method is applied to the computation of the interaction between highly nonlinear solitary waves and plane steep and gentle slopes. Kinematics of the waves is calculated during propagation and runup on a slope. In particular, the internal velocity field above the slope and the pressure force on the slope are computed in detail during runup and rundown of the wave. The results show features of the wave flow such as jet-like up-rush, stagnation point and breaking during backwash. A comparison is made with accurate experimental results (runup, surface elevations), with orther fully nonlinear solutions, and also with the predictions of the Shallow Water Wave Equation. The results show that the BEM used here is capable of accurately describing the wave flow and interaction with a plane slope(2.88° to 90°), in great detail.
Journal Article•
TL;DR: In this article, a series of experiments were carried out in the central test section of a 10 m long wave flume, to study the development and stability of sand bars, and two modes of sediment transport were identified: movement of fine grains in suspension by the residual mass transport circulation associated with a partially standing wave field and movement of both coarse and fine grains by vortex formation and shedding above small-scale ripples on the bed.
Abstract: A series of experiments was carried out in the central test section of a 10 m long wave flume, to study the development and stability of sand bars. Bar formation was initiated b (monochromatic) waves which were generated by a wave-maker at one end of the flume, and partially reflected by a beach at the other end. Sediment grains accumulated into bars with spacings equal to half the local surface wavelength. The positions of the bars relative to the nodes and antinodes of the wave envelope depended upon the type of sediment used. As the bars grew in size the reflection coefficient measured on their up-wave side increased significantly, suggesting a coupling between bar growth and the resonant (Bragg) reflection of the incident waves. In some experiments, stable equilibrium bar profiles were obtained. However, in others, the wave field became unstable, with wave breaking over the bar crests causing a flattening of the bed. Two modes of sediment transport were identified: movement of fine grains in suspension by the residual mass transport circulation associated with a partially standing wave field, and movement of both coarse and fine grains by vortex formation and shedding above small-scale ripples on the bed. When the net transport was such that coarser grains accumulated at the bar crests, this had a stabilising effect on the bars.
TL;DR: In this paper, full-field velocity measurements under the crest of a laboratory generated breaking wave are compared with a fully non-linear time-stepping numerical model and a plunging breaker is generated, on constant water depth, using the numerical model, then reproduced by matching wave amplitude timeseries at a position just before the breaking.
Abstract: Instantaneous, full-field velocity measurements under the crest of a laboratory generated breaking wave are presented and compared with a fully non-linear time-stepping numerical model. A plunging breaker is generated, on constant water depth, using the numerical model, then reproduced in a wave flume by matching wave amplitude timeseries at a position just before the breaking. The generation of the waves is achieved by means of a computer controlled wave paddle and measurements of the flow made with a full-field photographic technique (PIV). The photographic records of the flow are analysed on an automatic rig and the measurements are shown to compare well with the numerical calculations.
TL;DR: In this article, it is argued that due to the breaking of wind waves in deep water, the dissipation of energy is restricted to a range of frequencies ω > ωg, much higher than the frequency ωm of the dominant waves.
Abstract: Based on an interpretation of a field experiment it is argued that, due to breaking of wind waves in deep water, the dissipation of energy is restricted to a range of frequencies ω > ωg, much higher than the frequency ωm of the dominant waves In this dissipation range the spectrum has the form S(ω) = βg2ω−5 where g is the acceleration due to gravity and β = 0025 For spectral wave components at ω ≤ ωg, only a local balance between energy input from the wind and the weak, third-order, nonlinear interaction is important Asymptotically as ω ≫ ωm the wind input becomes unimportant, and the wave spectrum has the Kitaigorodskii form of a Kolgomorov analog S(ω) = 2aϵ0⅓ g4/3 ω−4 where ϵ0 is a constant flow of mean energy per unit surface area through the spectrum dissipated at high frequencies (when multiplied by g and water density ρw) From a method of M S Longuet-Higgins we estimate the magnitude of the dissipation (due to wave breaking) and find the Kolmogorov constant to be a ≈ 06 When a mode