Transmission and reflection of internal solitary waves incident upon a triangular barrier (original) (raw)

On the Reflectance of Uniform Slopes for Normally Incident Interfacial Solitary Waves

Journal of Physical Oceanography, 2007

The collision of interfacial solitary waves with sloping boundaries may provide an important energy source for mixing in coastal waters. Collision energetics have been studied in the laboratory for the idealized case of normal incidence upon uniform slopes. Before these results can be recast into an ocean parameterization, contradictory laboratory findings must be addressed, as must the possibility of a bias owing to laboratory sidewall effects. As a first step, the authors have revisited the laboratory results in the context of numerical simulations performed with a nonhydrostatic laterally averaged model. It is shown that the simulations and the laboratory measurements match closely, but only for simulations that incorporate sidewall friction. More laboratory measurements are called for, but in the meantime the numerical simulations done without sidewall friction suggest a tentative parameterization of the reflectance of interfacial solitary waves upon impact with uniform slopes.

On the breaking of internal solitary waves at a ridge

Journal of Fluid Mechanics, 2002

An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2-1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0-8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Numerical Experiments on the Breaking of Solitary Internal Wavesover a Slope–Shelf Topography

Journal of Physical Oceanography, 2002

A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope-shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth H s , a breaking event will arise whenever the wave amplitude a m is larger than 0.4(H s Ϫ H m), where H m is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of the propagating wave. At the latest stages of the evolution the overturned hydraulic jump transforms into a horizontal density intrusion (turbulent pulsating wall jet) propagating onto the shelf. The breaking criterion of the ISW over the slope was found. Over the range of examined parameters (0.52Њ Ͻ ␥ Ͻ 21.8Њ, where ␥ is the slope angle) the breaking event arises at the position with depth H b , when the nondimensional wave amplitude ϭ a m /(H b Ϫ H m) satisfies the condition ഡ 0.8Њ/␥ ϩ 0.4. If the water depth a a H s on a shelf is less than H b , a solitary wave breaks down before it penetrates into a shallow water zone; otherwise (at H s Ͼ H b) it passes as a dispersive wave tail onto the shelf without breaking.

Estimate of energy loss from internal solitary waves breaking on slopes

2021

Internal solitary waves (ISWs) emerge in the ocean and seas in various forms and break on the shelf zones in a variety of ways. This results in intensive mixing that affects processes such as biological productivity and sediment transport. As ISWs of depression propagate in a two-layer ocean, from the deep part onto a shelf, two mechanisms are significant: (1) the breaking of internal waves over bottom topography when fluid velocities exceed the wave phase speed that causes overturning of the rear face of the wave, and (2) the changing of polarity at the turning point where the depths of the upper and lower layers are equal. We assume that the parameters that describe the process of the interaction of ISWs in a two-layer fluid with an idealized shelf-slope topography are (1) the nondimensional wave amplitude, normalized on the upper-layer thickness; (2) the ratio of the height of the bottom layer on the shelf to the incident wave amplitude; and (3) the angle of the bottom inclination. Based on a proposed three-dimensional classification diagram, four types of wave propagation over the slopes are distinguished: the ISW propagates over the slope without changing polarity and wave breaking, the ISW changes polarity over the slope without wave breaking, the ISW breaks over the slope without changing polarity, and the ISW both breaks and changes polarity over the slope. The energy loss during ISW transformation over slopes with various angles was estimated using the results of 85 numerical experiments. "Hot spots" of high levels of energy loss were highlighted for an idealized bottom configuration that mimics the continental shelf in the Lufeng region in the South China Sea.

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

Journal of Geophysical Research: Oceans, 2020

We present a semi‐analytical model for predicting the breaking location of internal solitary waves (ISWs) over a sloping seabed. Our conceptual model is based on laboratory experiments, performed in a wave tank, that reproduce the ISW breaking mechanisms and show how the steepening of the trailing edge leads to verticalization of the wave profile during the shoaling phase. We derive the location of ISWs breaking, that is, the wave verticalization point, through two‐layer, interfacial theoretical models and conservation of wave mass. We apply our model to the case of tidally forced ISWs that are generated in the Strait of Messina (Central Mediterranean Sea), where northward traveling ISWs are expected to refract and break over the frontal slope of Capo Vaticano. Our application is then assessed through numerical investigations, which allow to consider realistic field conditions in terms of water column stratification and geometrical setting. Our results, and the expected ISW‐induced ...

Excitation of long internal waves by groups of short surface waves incident on a barrier

Journal of Fluid Mechanics, 1988

The effects of diffraction by a long barrier on second-order long waves forced by sinusoidally modulated short incident waves are examined for a two-layered model ocean. When the group velocity of the short waves lies between the phase velocities of the longest baroclinic and barotropic modes, long internal waves of the frequency equal to twice the modulational frequency of the short waves are found to radiate away from the edge ray which divides the geometrical shadow and the illuminated region. I n particular the baroclinic wave can penetrate the shadow. This penetration occurs when the internal long wavc is not resonated by short surface waves.

Large Internal Solitary Waves in Shallow Waters

2018

The propagation of finite amplitude internal waves over an uneven bottom is considered. One of the specific features of the large amplitude internal waves is the ability of the waves to carry fluid in the “trapped core” for a long distance. The velocity of particles in the “trapped core” is very close and, even, exceeds the wave speed. Such waves are detected in different parts of seas and oceans as internal waves of depression and elevation as well as short intrusions at interfaces. Laboratory experiments on the generation, interaction and decay of solitary waves in a two-layer fluid are discussed. Analytical and numerical solutions describing the evolution of internal waves in a shelf zone are constructed by the three-layer shallow water model. Laboratory investigations of the different types of internal waves (bottom, subsurface and interlayer waves) are demonstrating, that the model can be effectively applied to the numerical solution of unsteady wave motions, and the traveling ...

The transformation of an interfacial solitary wave of elevation at a bottom step

Nonlinear Processes in Geophysics, 2009

In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in the both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

Stratification effects on shoaling internal solitary waves

This combined numerical/laboratory study investigates the effect of stratification form on the shoaling characteristics of internal solitary waves propagating over a smooth, linear topographic slope. Three stratification types are investigated, namely (i) thin tanh (homogeneous upper and lower layers separated by a thin pycnocline), (ii) surface stratification (linearly stratified layer overlaying a homogeneous lower layer) and (iii) broad tanh (continuous density gradient throughout the water column). It is found that the form of stratification affects the breaking type associated with the shoaling wave. In the thin tanh stratification, good agreement is seen with past studies. Waves over the shallowest slopes undergo fission. Over steeper slopes, the breaking type changes from surging, through collapsing to plunging with increasing wave steepness A w /L w for a given topographic slope, where A w and L w are incident wave amplitude and wavelength, respectively. In the surface stratification regime, the breaking classification differs from the thin tanh stratification. Plunging dynamics is inhibited by the density gradient throughout the upper layer, instead collapsing-type breakers form for the equivalent location in parameter space in the thin tanh stratification. In the broad tanh profile regime, plunging dynamics is likewise inhibited and the near-bottom density gradient prevents the collapsing dynamics. Instead, all waves either fission or form surging breakers. As wave steepness in the broad tanh stratification increases, the bolus formed by surging exhibits evidence of Kelvin-Helmholtz instabilities on its upper boundary. In both two-and three-dimensional simulations, billow size grows with increasing wave steepness, dynamics not previously observed in the literature.

Interaction of a large amplitude interfacial solitary wave of depression with a bottom step

Physics of Fluids, 2010

The dynamics and energy balance of the transformation of a large amplitude interfacial solitary wave of depression transformed at the bottom step are studied. Three simulations are described using the non-hydrostatic extension of the Princeton Ocean Model (POM), based on the fully nonlinear Navier-Stokes equations in the Boussinesq approximation. The first simulation is when the ratio of the step height to the lower layer thickness is about 0.4 and the incident wave amplitude is less than the limiting value estimated for a Gardner soliton. It shows the applicability of the weakly nonlinear model (the extended Korteweg-de Vries or Gardner equation) to describe the transformation of a strongly nonlinear wave in this case. In the second simulation the incident wave amplitude is increased and is then described by the Miyata-Choi-Camassa solitary wave solution. In this case, the process of wave transformation is accompanied by shear instability and the formation of Kelvin-Helmholtz billows that results in a thickening of the interface layer. In the third simulation, the ratio of the step height to the thickness of the lower layer is 0.8, and then the same Miyata-Choi-Camassa solitary wave passes over the step, but undergoes stronger reflection and mixing between the layers although Kelvin-Helmholtz instability is absent. The energy budget of the wave transformation is calculated. It is shown that the energy loss in the vicinity of the step