Solitary waves perturbed by a broad sill. Part 1. Propagation across the sill

2019 ◽  
Vol 880 ◽  
pp. 916-934 ◽  
Author(s):  
Harrison T.-S. Ko ◽  
Harry Yeh
Keyword(s):  
Energy Dissipation ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Wave Amplitude ◽  
The State ◽  
Transmitted Wave ◽  
Wave State ◽  
Transmitted Waves

Stability of a solitary wave disturbed by a submerged flat sill is investigated experimentally. For sills narrow compared with the solitary wave, the transmitted waves are found to be unaffected in waveform and amplitude. A wider sill disturbs the solitary wave resulting in the formation of a dispersive wavetrain following the transmitted wave. In some cases, the wave amplitude recovers, despite being perturbed, to the state of an unobstructed solitary-wave state at a certain distance beyond the sill. Wider sills cause wave breaking that occurs over the sill or, in some cases, after the wave passes through the sill. Details of waveform transformation leading toward the breaking and subsequent energy dissipation are discussed.

Estimating energy dissipation in internal solitary waves breaking on slopes

2021 ◽  
Author(s):  
Kateryna Terletska ◽  
Vladіmir Maderich ◽  
Tatiana Talipova
Keyword(s):  
Energy Dissipation ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Wave Amplitude ◽  
Hot Spot ◽  
Slope Angle ◽  
Bottom Layer ◽  
Internal Solitary Waves ◽  
Coastal Zones ◽  
Waves Interaction

<p>The shoaling mechanisms of internal solitary waves that propagate horizontally are an important source of mixing and transport in the coastal zones. Numerical modelling, llaboratory experiments and observations are needed for understanding wave energetics, especially energy transformation during waves interaction with the slopes. Two shoaling mechanisms are important during interaction with the slope: (i) wave breaking that results in mixing and dissipation, (ii) changing of the polarity of the initial wave of depression on the slope. Classification based on regimes of interaction with the slope was presented in [1]. Four zones were separated in αβγ (γ - is slope angle, α-  is the non-dimensional wave amplitude (wave amplitude normalized on the thermocline thickness) and β – is the blocking parameter that is the ratio of the height of the bottom layer on the shelf to the incident wave amplitude) classification diagram: (I) without changing polarity and wave breaking, (II) changing polarity without breaking; (III) wave breaking without changing polarity; (IV) wave breaking with changing polarity. It was shown that results of field, laboratory and numerical experiments are in good agreement with proposed classification.  In the present study we estimate energy dissipation for all the types of interaction and present the algorithm for building a zone map with a ‘hot spot’ of energy dissipation for real slopes in the ocean.</p><p> </p><p>[1] K Terletska, BH Choi, V Maderich, T Talipova  Classification of internal waves shoaling over slope-shelf topography RUSSIAN JOURNAL OF EARTH SCIENCES vol. 20, 4, 2020, doi: 10.2205/2020ES000730</p>

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

Experimental Investigation on Solitary Wave Interaction With Vertical Porous Barriers

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Vivek Francis ◽  
Balaji Ramakrishnan ◽  
Murray Rudman
Keyword(s):  
Energy Dissipation ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Interaction ◽  
Coastal Protection ◽  
Tsunami Waves ◽  
Porous Barrier ◽  
Porous Barriers ◽  
Run Up ◽  
Solitary Wave Interaction

Abstract Tsunami waves pose a threat to the coastal zone, and numerous studies have been carried out in the past to understand them. Solitary waves have been extensively used in research because they approximate certain important characteristics of tsunami waves. The present study focusses on the interaction and run-up of solitary waves on coastal protection structures in the form of thin, rigid vertical porous barriers with special attention given to the degree of energy dissipation. To understand the physics of energy dissipation, solitary wave interaction with a porous barrier has been studied from the viewpoint of energy balance. Based on this, a relationship for the wave energy dissipation has been developed. The experimental data show that the plate porosity that gives the optimal energy dissipation lies within the 10–20% range. From the experiments, the phase shift that the solitary wave undergoes upon interaction with the porous barrier models has also been recorded. In addition, a formula is proposed for maximum wave run-up on the porous barrier, which should be useful in the planning, design, construction, and maintenance of coastal protection structures.

Propagation of solitary waves through significantly curved shallow water channels

1998 ◽  
Vol 362 ◽  
pp. 157-176 ◽  
Author(s):  
AIMIN SHI ◽  
MICHELLE H. TENG ◽  
THEODORE Y. WU
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Wave Amplitude ◽  
Water Channels ◽  
Numerical Results ◽  
Channel Width ◽  
Boussinesq Model ◽  
Reflected Wave ◽  
Transmission And Reflection

Propagation of solitary waves in curved shallow water channels of constant depth and width is investigated by carrying out numerical simulations based on the generalized weakly nonlinear and weakly dispersive Boussinesq model. The objective is to investigate the effects of channel width and bending sharpness on the transmission and reflection of long waves propagating through significantly curved channels. Our numerical results show that, when travelling through narrow channel bends including both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted almost completely with little reflection and scattering. For wide channel bends, we find that, if the bend is rounded and smooth, a solitary wave is still fully transmitted with little backward reflection, but the transmitted wave will no longer preserve the shape of the original solitary wave but will disintegrate into several smaller waves. For solitary waves travelling through wide sharp-cornered 90°-bends, wave reflection is seen to be very significant, and the wider the channel bend, the stronger the reflected wave amplitude. Our numerical results for waves in sharp-cornered 90°-bends revealed a similarity relationship which indicates that the ratios of the transmitted and reflected wave amplitude, excess mass and energy to the original wave amplitude, mass and energy all depend on one single dimensionless parameter, namely the ratio of the channel width b to the effective wavelength λe. Quantitative results for predicting wave transmission and reflection based on b/λe are presented.

Breaking and broadening of internal solitary waves

2000 ◽  
Vol 413 ◽  
pp. 181-217 ◽  
Author(s):  
JOHN GRUE ◽  
ATLE JENSEN ◽  
PER-OLAV RUSÅS ◽  
J. KRISTIAN SVEEN
Keyword(s):  
Solitary Waves ◽  
Wave Breaking ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Constant Density ◽  
Image Velocimetry ◽  
The Waves

Solitary waves propagating horizontally in a stratified fluid are investigated. The fluid has a shallow layer with linear stratification and a deep layer with constant density. The investigation is both experimental and theoretical. Detailed measurements of the velocities induced by the waves are facilitated by particle tracking velocimetry (PTV) and particle image velocimetry (PIV). Particular attention is paid to the role of wave breaking which is observed in the experiments. Incipient breaking is found to take place for moderately large waves in the form of the generation of vortices in the leading part of the waves. The maximal induced fluid velocity close to the free surface is then about 80% of the wave speed, and the wave amplitude is about half of the depth of the stratified layer. Wave amplitude is defined as the maximal excursion of the stratified layer. The breaking increases in power with increasing wave amplitude. The magnitude of the induced fluid velocity in the large waves is found to be approximately bounded by the wave speed. The breaking introduces a broadening of the waves. In the experiments a maximal amplitude and speed of the waves are obtained. A theoretical fully nonlinear two-layer model is developed in parallel with the experiments. In this model the fluid motion is assumed to be steady in a frame of reference moving with the wave. The Brunt-Väisälä frequency is constant in the layer with linear stratification and zero in the other. A mathematical solution is obtained by means of integral equations. Experiments and theory show good agreement up to breaking. An approximately linear relationship between the wave speed and amplitude is found both in the theory and the experiments and also when wave breaking is observed in the latter. The upper bound of the fluid velocity and the broadening of the waves, observed in the experiments, are not predicted by the theory, however. There was always found to be excursion of the solitary waves into the layer with constant density, irrespective of the ratio between the depths of the layers.

On the breaking of internal solitary waves at a ridge

2002 ◽  
Vol 469 ◽  
pp. 161-188 ◽  
Author(s):  
J. KRISTIAN SVEEN ◽  
YAKUN GUO ◽  
PETER A. DAVIES ◽  
JOHN GRUE
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Lower Layer ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Internal Solitary Wave ◽  
Layer Thickness Ratio ◽  
Transmitted Waves ◽  
Ridge Height ◽  
Experimental Laboratory

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.

scholarly journals Estimate of energy loss from internal solitary waves breaking on slopes

2021 ◽  
Author(s):  
Kateryna Terletska ◽  
Vladimir Maderich ◽  
Tatiana Talipova
Keyword(s):  
Energy Loss ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Numerical Experiments ◽  
Wave Amplitude ◽  
Three Dimensional ◽  
Bottom Layer ◽  
Internal Solitary Waves ◽  
Weakly Nonlinear ◽  
Shelf Slope

Abstract. Internal solitary waves (ISW) emerge in the ocean and seas in different forms and break on the shelf zones in a variety of ways. Their breaking on slopes can produce intensive mixing that produces such process as biological productivity and sediment transport. Mechanisms of ISW of depression interaction with the slopes related to breaking and changing polarity as they shoal. We assume that parameters that described the process of interaction of ISW in a two-layer fluid with the idealised shelf-slope are: the non-dimensional wave amplitude α (wave amplitude normalized on the upper layer thickness), the ratio of the height of the bottom layer on the shelf to the incident wave amplitude β and angle γ. Based on three-dimensional αβγ classification diagram with four types of interaction with the slopes it was discussed: (1) ISW propagates over slope without changing polarity and wave breaking; (2) ISW changes polarity over slope without breaking; (3) ISW breaks over slope without changing polarity; (4) ISW both breaks and change polarity over the slope. Relations between the parameters α,β,γ for each regime were obtained using the empirical condition for wave breaking and weakly nonlinear theory for the criterion of changing the polarity of the wave. In the present paper the α,β,γ diagram was validated for idealised real scale topography configurations. Results of the numerical experiments that were carried out in the present paper and results of field and laboratory experiments from other papers are in good agreement with proposed classification and estimations. Based on 85 numerical experiments ISWs energy loss during interaction with slope topography with 0.5° < γ < 90° was estimated. Hot spots zones of high levels of energy loss were shown for idealized configuration that mimics continental shelf at Lufeng Region SCS.

scholarly journals Numerical Simulation for the Evolution of Internal Solitary Waves Propagating over Slope Topography

2021 ◽  
Vol 9 (11) ◽  
pp. 1224
Author(s):  
Yingjie Hu ◽  
Li Zou ◽  
Xinyu Ma ◽  
Zhe Sun ◽  
Aimin Wang ◽  
...  
Keyword(s):  
Numerical Model ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Amplitude ◽  
Domain Boundary ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
Initial Amplitude ◽  
Nonlinear Potential ◽  
Slope Topography

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

Comment on ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’

2014 ◽  
Vol 80 (3) ◽  
pp. 513-516
Author(s):  
Frank Verheest
Keyword(s):  
Shock Wave ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Plasma Phys ◽  
Theoretical Underpinning ◽  
Pair Plasma ◽  
Electrons And Positrons ◽  
Small Dissipation ◽  
Pseudopotential Approach ◽  
Wave Properties

In a recent paper ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’, Malekolkalami and Mohammadi investigate nonlinear electrostatic solitary waves in a plasma comprising adiabatic electrons and positrons, and a stationary ion background. The paper contains two parts: First, the solitary wave properties are discussed through a pseudopotential approach, and then the influence of a small dissipation is intuitively sketched without theoretical underpinning. Small dissipation is claimed to lead to a shock wave whose wavelength is determined by linear oscillator analysis. Unfortunately, there are errors and inconsistencies in both the parts, and their combination is incoherent.

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