Showing papers on "Breaking wave published in 2006"

Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves

Abstract: Here we discuss the statistical properties of the surface elevation for long crested waves characterized by Jonswap spectra with random phases. Experiments are performed in deep water conditions in one of the largest wave tank facilities in the world. We show that for long-crested waves and for large values of the Benjamin–Feir index, the second order theory is not adequate to describe the tails of the probability density function of wave crests and wave heights. We show that the probability of finding an extreme wave can be underestimated by more than one order of magnitude if second order theory is considered. We explain these observed deviations in terms of the modulational instability mechanism that for large BFI can take place in random wave spectra.

Wave impact loads: The role of the flip-through

Abstract: The impact of waves upon a vertical, rigid wall during sloshing is analyzed with specific focus on the modes that lead to the generation of a flip-through [M. J. Cooker and D. H. Peregrine, “A model for breaking wave impact pressures,” in Proceedings of the 22nd International Conference on Coastal Engineering (ASCE, Delft, 1990), Vol. 2, pp. 1473–1486]. Experimental data, based on a time-resolved particle image velocimetry technique and on a novel free-surface tracking method [M. Miozzi, “Particle image velocimetry using feature tracking and Delaunay tessellation,” in Proceedings of the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (2004)], are used to characterize the details of the flip-through dynamics while wave loads are computed by integrating the experimental pressure distributions. Three different flip-through modes are observed and studied in dependence on the amount and modes of air trapping. No air entrapment characterizes a “mode (a) flip-through,” engulfm...

On the Interaction of Surface Waves and Upper Ocean Turbulence

Abstract: The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.

Spectral Distribution of Energy Dissipation of Wind-Generated Waves due to Dominant Wave Breaking

Abstract: This paper considers an experimental attempt to estimate the spectral distribution of the dissipation due to breaking of dominant waves. A field wave record with an approximately 50% dominant-breaking rate was analyzed. Segments of the record, comprising sequences of breaking waves, were used to obtain the “breaking spectrum,” and segments of nonbreaking waves were used to obtain the “nonbreaking spectrum.” The clear visible difference between the two spectra was attributed to the dissipation due to breaking. This assumption was supported by independent measurements of total dissipation of kinetic energy in the water column at the measurement location. It is shown that the dominant breaking causes energy dissipation throughout the entire spectrum at scales smaller than the spectral peak waves. The dissipation rate at each frequency is linear in terms of the wave spectral density at that frequency, with a correction for the directional spectral width. A formulation for the spectral dissipation fun...

Variational formulations for steady water waves with vorticity

Abstract: For free-surface water flows with a vorticity that is monotone with depth, we show that any critical point of a functional representing the total energy of the flow adjusted with a measure of the vorticity, subject to the constraints of fixed mass and horizontal momentum, is a steady water wave.

Nearshore Wave Modeling with High-Order Boussinesq-Type Equations

Abstract: The accuracy of using high-order Boussinesq-type models as compared to the typical order models is examined in this paper. The high-order model used is the two-layer model of Lynett and Liu in 2004, which captures both linear and nonlinear wave evolution up to kh≈6 . The physical situations examined all involve nearshore breaking, and an eddy-viscosity type breaking model is adopted for the two-layer model. One-horizontal dimension setups are the focus of this paper. It is shown that high-order models show significant benefit very near to the breaker line. For regular incident waves, the overshoaling seen in the one-layer (“fully nonlinear” extended Boussinesq) model is due to rapid increase of energy in the fifth and higher harmonics. These high-order nonlinear components are captured well in the two-layer model. The two-layer model also exhibits a noticeable accuracy increase for cnoidal waves breaking on a slope. For regular wave evolution over a bar, the high-order models are in good agreement with ex...

Short light pulse amplification and compression by stimulated Brillouin scattering in plasmas in the strong coupling regime

Abstract: Short light pulse amplification using the stimulated Brillouin backscattering mechanism is considered. The novel feature is that the interaction process takes place in the strongly coupled regime and therefore the pulse compression is not limited by the ion-acoustic wave period. The mechanism is very efficient due to the large ratio of light frequency to the characteristic ion-acoustic wave frequency. Although large-amplitude ion-acoustic waves are generated and subsequent wave breaking takes place, the fluid and kinetic nonlinearities do not intervene with the amplification itself.

Long time interaction of envelope solitons and freak wave formations

Abstract: This paper concerns long time interaction of envelope solitary gravity waves propagating at the surface of a two-dimensional deep fluid in potential flow. Fully nonlinear numerical simulations show how an initially long wave group slowly splits into a number of solitary wave groups. In the example presented, three large wave events are formed during the evolution. They occur during a time scale that is beyond the time range of validity of simplified equations like the nonlinear Schrodinger (NLS) equation or modifications of this equation. A Fourier analysis shows that these large wave events are caused by significant transfer to side-band modes of the carrier waves. Temporary downshiftings of the dominant wavenumber of the spectrum coincide with the formation large wave events. The wave slope at maximal amplifications is about three times higher than the initial wave slope. The results show how interacting solitary wave groups that emerge from a long wave packet can produce freak wave events. Our reference numerical simulation are performed with the fully nonlinear model of Clamond and Grue [D. Clamond, J. Grue, A fast method for fully nonlinear water wave computations, J. Fluid Mech. 447 (2001) 337–355]. The results of this model are compared with that of two weakly nonlinear models, the NLS equation and its higher-order extension derived by Trulsen et al. [K. Trulsen, I. Kliakhandler, K.B. Dysthe, M.G. Velarde, On weakly nonlinear modulation of waves on deep water, Phys. Fluids 12 (10) (2000) 2432–2437]. They are also compared with the results obtained with a high-order spectral method (HOSM) based on the formulation of West et al. [B.J. West, K.A. Brueckner, R.S. Janda, A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, J. Geophys. Res. 92 (C11) (1987) 11 803–11 824]. An important issue concerning the representation and the treatment of the vertical velocity in the HOSM formulation is highlighted here for the study of long-time evolutions.

Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling

Abstract: In this paper a truly incompressible version of the smoothed particle hydrodynamics (SPH) method is presented to investigate the surface wave overtopping. SPH is a pure Lagrangian approach which can handle large deformations of the free surface with high accuracy. The governing equations are solved based on the SPH particle interaction models and the incompressible algorithm of pressure projection is implemented by enforcing the constant particle density. The two-equation k–e model is an effective way of dealing with the turbulence and vortices during wave breaking and overtopping and it is coupled with the incompressible SPH numerical scheme. The SPH model is employed to reproduce the experiment and computations of wave overtopping of a sloping sea wall. The computations are validated against the experimental and numerical data found in the literatures and good agreement is observed. Besides, the convergence behaviour of the numerical scheme and the effects of particle spacing refinement and turbulence modelling on the simulation results are also investigated in further detail. The sensitivity of the computed wave breaking and overtopping on these issues is discussed and clarified. Copyright © 2005 John Wiley & Sons, Ltd.

Numerical study of three-dimensional overturning waves in shallow water

Abstract: Simulations in a three-dimensional numerical wave tank are performed to investigate the shoaling and breaking of solitary waves over a sloping ridge. The numerical model solves fully nonlinear potential flow equations with a high-order boundary-element method combined with an explicit time-integration method, expressed in a mixed Eulerian-Lagrangian formulation. Analyses of shoaling and breaking-wave profiles and kinematics (both on the free surface and within the flow) are carried out. It is observed that the transverse modulation of the ridge topography induces three-dimensional effects on the time evolution, shape and kinematics of breaking waves. Comparisons of two- and three-dimensional results in the middle cross-section of the ridge, however, show remarkable similarities, especially for the shape and dynamics of the plunging jet.

Radar scattering of the ocean surface and sea-roughness properties : A combined analysis from dual-polarizations airborne radar observations and models in C band

Abstract: [1] An analysis of radar observations in C band combined with models is proposed to study some of the ocean surface properties and their relation with the sea surface backscatter. The electromagnetic part of the models is of different kinds: composite Bragg model with or without including effect of wave breaking zones on the normalized radar cross-section (NRCS), geometrical optics approximation and small-slope approximation model. The surface description is based on the wave spectrum proposed by Kudryavtsev et al. (2003), but tests with the spectrum of Elfouhaily et al. (1997) are also discussed to assess our conclusions. The originality is to use not only the NRCS in HH and VV polarizations, but also their difference in linear units. First, we show that the upwind-to-downwind anisotropy of the radar signal cannot be explained entirely by the modulation of Bragg waves by longer surface waves, but that an additional nonpolarized contribution must be invoked to explain it, consistently with scattering from zones of enhanced roughness associated with breaking waves. Then, combining a composite model and observations in the two polarizations, we assess the contribution of the nonpolarized backscatter on the total NRCS. Finally, the proposed full model, which takes into account the nonpolarized contribution over breaking zones, gives good agreement with the observed polarization ratio and with the NRCS in each polarization.

Plane Impulse Waves in Reservoirs

Abstract: The characteristics of impulse waves generated in reservoirs by the impact of variable density mass flows were assessed using two-dimensional model experimentation. Particle image velocimetry (PIV) was applied within the wave generation area at the slide impact location and the water wave profiles were measured by seven successive capacitance wave gages. The maximum relative wave amplitude and the normalized wave amplitude of the propagating wave train were correlated with the dimensionless slide quantities and the relative propagation distance, respectively. The impact Froude number was identified as the dominant parameter for slow impacting slides, whereas the water depth and the slide thickness governed the maximum possible wave amplitude for large impact Froude numbers. Four wave types were distinguished due to three different levels of wave nonlinearity associated with variable impact Froude numbers, relative slide densities, and characteristic slide geometries: nonlinear transient bore, transition wave, oscillatory wave, and nonbreaking solitary wave. Moreover, the density effect on the wave generation process was investigated with small impact Froude numbers using sequential PIV velocity vector fields.

Drift and mixing under the ocean surface: A coherent one-dimensional description with application to unstratified conditions

Abstract: [1] Waves have many effects on near-surface dynamics: Breaking waves enhance mixing, waves are associated with a Lagrangian mean drift (the Stokes drift), waves act on the mean flow by creating Langmuir circulations and a return flow opposite to the Stokes drift, and, last but not least, waves modify the atmospheric surface roughness. A realistic ocean model is proposed to embrace all these aspects, focusing on near-surface mixing and surface drift associated with the wind and generated waves. The model is based on the generalized Lagrangian mean that separates the momentum into a wave pseudomomentum and a quasi-Eulerian momentum. A wave spectrum with a reasonably high frequency range is used to compute the Stokes drift. A turbulent closure scheme based on a single evolution equation for the turbulent kinetic energy includes the mixing due to breaking wave effects and wave-turbulence interactions. The roughness length of the closure scheme is adjusted using observations of turbulent kinetic energy near the surface. The model is applied to unstratified and horizontally uniform conditions, showing good agreement with observations of strongly mixed quasi-Eulerian currents near the surface when waves are developed. Model results suggest that a strong surface shear persists in the drift current because of the Stokes drift contribution. In the present model the surface drift only reaches 1.5% of the wind speed. It is argued that stratification and the properties of drifting objects may lead to a supplementary drift as large as 1% of the wind speed.

Gravity wave influence on the global structure of the diurnal tide in the mesosphere and lower thermosphere

Abstract: [1] Observations of the diurnal tide from instruments aboard the Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics (TIMED) explorer and from the Upper Atmosphere Research Satellite (UARS) show that the vertical wavelength of the tide is significantly shorter than what is predicted by tidal theory. The observed vertical structure of the tide can be reproduced in a mechanistic model by including gravity wave interaction. The model tide amplitude and phase are sensitive to the amplitude and phase of the diurnal component of momentum forcing that arises from gravity wave breaking. The phase of the momentum forcing relative to the tide determines whether the tide amplitude is increased or diminished by gravity wave forcing, while the amplitude of the momentum forcing determines how rapidly the tide phase will change with height. The momentum forcing profile is shaped by the structure of the gravity wave source spectrum. By comparing both the model tide amplitude and phase profiles to observations, we can provide constraints on both the gravity wave source spectrum that should be used in a gravity wave parameterization scheme and on the eddy diffusion that acts on the tide. We examine differences between the effects that two gravity wave schemes have on the tide. The role that gravity waves may play in producing tide variability is discussed in light of the results presented here.

On the effect of sea drops on the atmospheric boundary layer

Abstract: [1] One of the possible mechanisms responsible for the reduction of the sea surface drag at high winds is explored. The mechanism is based on the direct effect of sea drops (as heavy particles) on the turbulent mixing. If assumed that sea drops are ejected upward from the sea surface, no significant effect can be found. A more realistic picture presumes that the spume drops (resulting from a mechanical tearing of wave crests) are ejected “horizontally” at altitudes of breaking crests. A model of the spume drops generation is proposed. The spume drops, being torn off from breaking crests and sprayed inside the airflow, significantly affect the surface drag. At highest model wind speeds (60–80 m/s) the model actually predicts an effect of the “slippery surface” when the drag coefficient is reduced in about 10 times. A comparison with available observations is given.

Instability mechanisms of a two-dimensional progressive internal gravity wave

Abstract: We present a detailed investigation of the parametric subharmonic resonance mechanism that leads a plane, monochromatic, small-amplitude internal gravity wave, also referred to as the primary wave, to instability. Resonant wave interaction theory is used to derive a simple kinematic model for the parametrically forced perturbation, and direct numerical simulations of the Boussinesq equations in a vertical plane permit the nonlinear simulation of the internal gravity wave field. The processes that eventually drive the wave field to breaking are also addressed.We show that parametric instability may be viewed as an optimized scenario for drawing energy from the primary wave, that is, from a periodic flow with both oscillating shear and density gradient. Optimal energy exchange maximizing perturbation growth is realized when the perturbation has a definite spatio-temporal structure: its energy is phase-locked with the vorticity of the primary wave. This organization allows the perturbation energy to alternate between kinetic form when locally the primary wave shear is negative, then maximizing kinetic energy extraction from the primary wave, and potential form when the primary wave shear is positive, then minimizing the reverse transfer to that wave. The perturbation potential energy increases through the primary wave density gradient whether the latter is positive, that is when the medium is of reduced static stability, or negative (increased static stability). When the primary wave amplitude is small, all energy transfer terms are predicted well by the kinematic model. One important result is that the rate of potential energy transfer from the primary wave to the perturbation is always larger than the rate of kinetic energy transfer, whatever the primary wave.As the perturbation amplifies, overturned isopycnals first appear in reduced static stability regions, implying that the total field should become unstable through a buoyancy induced (or Rayleigh–Taylor) instability. Hence, a two-dimensional model is no longer valid for studying the subsequent flow development.

Energy propagation of thermal waves

Abstract: Although waves are ubiquitous in nature it is difficult to give a precise and unambiguous definition of what a wave is. Actually the distinction between wave-like and non-wave-like behaviour can be fuzzy, as it is the case of a solid sample excited by a periodic heat source. The resulting temperature oscillations inside the sample have the same mathematical expression as highly damped waves, the so-called thermal waves. The aim of this paper is to stress the energy propagation as the key to affirm whether there is wave motion. In this way it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy. This result has been obtained not only in the frame of the parabolic heat conduction equation that evidences the diffusive nature of the heat conduction process, but also in the frame of the hyperbolic heat conduction equation, that is a wave equation.

Gravity wave breaking, secondary wave generation, and mixing above deep convection in a three-dimensional cloud model

Abstract: [1] This paper documents the breakdown of gravity waves generated by deep convection in a three-dimensional cloud-resolving model. The convection generates gravity waves that propagate into the lower stratosphere, with horizontal wavelengths between 5 and 10 km. Above-cloud wind shear causes part of the spectrum of these waves to break, inducing overturning. The model grid spacing is small enough (150 m) that the gravity waves are well resolved, and the turbulent cascade induced by the breakdown is partially resolved. Previous model simulations of wave breakdown above deep convection, at this resolution, have only been achieved in two-dimensional models. The wave breakdown generates secondary waves, which have much shorter horizontal wavelengths, and different propagation characteristics compared to the primary waves. Secondary wave generation in the lower stratosphere above deep convection has not been identified in previous studies. The wave breakdown also induces irreversible mixing, which is quantified in terms of the vertical transport of water vapor.

Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia–Gravity Waves from an Intense Mesoscale Cyclone

Abstract: The spontaneous radiation of spiral inertia–gravity (IG) waves from monotonic cyclones is reexamined. Such radiation can occur most significantly in a parameter regime that includes strong supercell mesocyclones and hurricanes. First, linear theory is reviewed. In linear theory, a generic deformation of the cyclone excites discrete vortex Rossby (VR) waves. Each VR wave emits a frequency-matched spiral IG wave into the environment. The emission has positive feedback on the VR wave, causing both to grow. However, the VR wave also deposits wave activity into its critical layer at the radius r * . If the radial gradient of potential vorticity at r * exceeds a threshold, critical layer absorption suppresses the radiative instability. On the other hand, numerical simulations of a shallow-water cyclone show that nonlinear changes to the critical layer can revive a damped VR wave and its radiation field after a brief period of decay. For such revival, it suffices that b/| | 1. This inequality contains two characteristic frequencies. The denominator | | is the absolute value of the (negative) growth rate of the damped wave. The numerator b is the mixing rate of the critical layer, which is proportional to the square root of the initial wave amplitude. After damping is reversed, the radiative VR wave exhibits undulatory growth. Analysis shows that growth proceeds because radiation steadily removes negative wave activity from the cyclone. Secondary amplitude oscillations are due to back-and-forth exchanges of positive wave activity between the VR wave and its critical layer.

Large-Scale Experiments on Pore Pressure Generation underneath a Caisson Breakwater

Abstract: Results of large-scale model experiments in a wave flume are discussed. These experiments are concerned with the study of the generation of transient or instantaneous and residual pore pressure in a seabed beneath a caisson breakwater subjected to both pulsating and breaking wave loads. The simulated seabed and drainage conditions correspond to those encountered in a loose sand bed with thin clay or silt layers. Even under such unfavorable conditions total liquefaction due to residual pore pressures could not occur during the experiments. It is shown that the residual pore pressure is essentially generated by the caisson motions due to breaking wave loads and that they are closely related to residual soil deformations, which may lead to the failure of the breakwater.

Passive Acoustic Determination of Wave-Breaking Events and Their Severity across the Spectrum

Abstract: A passive acoustic method of detecting breaking waves of different scales has been developed. The method also showed promise for measuring breaking severity. Sounds were measured by a subsurface hydrophone in various wind and wave states. A video record of the surface was made simultaneously. Individual sound pulses corresponding to the many individual bubble formations during wave-breaking events typically last only a few tens of milliseconds. Each time a sound-level threshold was exceeded, the acoustic signal was captured over a brief window typical of a bubble formation pulse, registering one count. Each pulse was also analyzed to determine the likely bubble size generating the pulse. Using the time series of counts and visual observations of the video record, the sound-level threshold that detected bubble formations at a rate optimally discriminating between breaking and nonbreaking waves was determined by a classification-accuracy analysis. This diagnosis of breaking waves was found to be ap...

Breaking waves over a mild gravel slope: Experimental and numerical analysis

Abstract: [1] An experimental and numerical study of the effects of a gravel slope on wave shoaling and breaking is presented herein. In the laboratory experiments, fluid velocities, pressure and water surface elevations were measured. Experiments were conducted for both spilling and plunging breakers and for gravel slopes with different gravel sizes. Since gravel slopes caused additional energy dissipation, wave heights in the shoaling zone as well as at the breaking point were reduced. On the other hand, the mean free surface setup inside the surf zone increased. It was also observed that the gravel slope had a stronger influence on the vertical profile of undertow under spilling breaker than on that under a plunging breaker. Moreover, the undertow became weaker over a gravel slope with a larger gravel size. Outside the surf zone, turbulent velocities near the gravel slope were relatively high because of the bottom roughness and percolation. Inside the surf zone, turbulence generated by wave breaking dominated over the gravel bed generated turbulence. The vertical flow induced by the gravel slope changed the turbulence pattern only at cross sections very close to the shoreline. Numerical simulations of the wave breaking processes over a gravel slope were performed. The numerical model was tested by comparing numerical results with experimental data. The model accurately simulated the mean flow quantities. The magnitude of turbulence and turbulence characteristics were also simulated reasonably well.

Solitary wave transformation, breaking and run-up at a beach

Abstract: A validated one-dimensional Boussinesq–non-linear shallow water equations numerical model was used to investigate the interaction of solitary waves with beaches. The numerical model requires two adjustable parameters: the bed friction coefficient and a wave breaking parameter. Excellent agreement was achieved between the numerical predictions of solitary wave transformation and run-up at a plane beach with two sets of high-quality laboratory measurements: one a large number of experiments in a wave flume by Synolakis, the other in the UK Coastal Research Facility. A parameter study investigated the effect of uniform offshore water depth, bed friction and bed slope on solitary wave run-up. A uniform water depth may be associated with a continental shelf region. The non-dimensional run-up was found to be an asymptotic function of non-dimensional wave amplitude at high and low values of initial wave steepness. Both asymptotes scale as (R/ho)∼α(Ao/ho)β where R is run-up (defined as the vertical elevation reac...