Interaction Of Internal Solitary Waves Research Articles

Interaction of mode-one internal solitary waves of opposite polarity in double-pycnocline stratifications

Numerical simulations of the interaction of internal solitary waves (ISWs) of opposite polarity are conducted by solving the incompressible Euler equations under the Boussinesq approximation. A double-pycnocline stratification is used. A method to determine when ISWs of both polarities exist is also presented. The simulations confirm previous work that the interaction of waves of the same polarity are soliton-like; however, here it is shown that when a fast ISW with the same polarity as a Korteweg–de Vries (KdV) solitary wave catches up and interacts with a slower ISW of opposite polarity, the interaction can be far from soliton-like. The energy in the fast KdV-polarity wave can increase by more than a factor of 5 while the energy in the slower negative-KdV-polarity wave can decrease by 50 %. Large trailing wave trains may be generated and in some cases multiple ISWs with KdV polarity may be formed by the interaction.

Investigation of the interaction of internal solitary waves with the slope-shelf topography

In this paper, internal solitary waves (ISWs) propagating over shelf topographies are studied based on numerical experiments conducted according to the lock-release method. The wave generation, propagation, and interactions with slope-shelf topography are investigated in a wave tank. The primary features of the propagation of ISWs on the slope are assessed. Shear and advection instabilities are observed in the current simulations in some cases with 1.29 < Bs < 1.75 (Bs is defined as the ratio of layer water depth on the shelf to the ISW amplitude). The induced density flow contributes to the growth of potential energy by dilution and stripping, primarily through its head, which is one of the factors used to enhance the mixing efficiency. In addition, the obtained results are compared with those of previous experiments conducted by other researchers, while considering the differences in local topography. The comparison reveals that local topography is a reason for the experimental differences of some research studies. ISW breaking on a slope is strongly influenced by the initial flow field of the slope, which may lead to differences in the prediction of the breaking point by using boundary layer separation as a criterion. As the incident wave amplitude increases, the location of the breaking point shifts downward and its magnitude gradually decreases.

Numerical modeling of energy dissipation of internal solitary waves encountering step topography

In this study, we conducted simulation experiments using a large-eddy simulation method to examine the interaction of internal solitary waves (ISWs) with step topography. We investigated the propagation, transmission, reflection, and breaking of depression ISWs. The features of ISW depend on the geometrical parameters of the step topography that define the initial setting. The relationships between the ISWs geometric and energy loss features as well as the initial setting parameters were analyzed; related empirical relations were developed. Following the analysis of the vortex changes during the process of wave-topography interaction, the different breaking processes and their development rules were discussed. The results showed that, as the obstacle height increased, the degree of energy conversion during the interaction increased. There is no explicit relationship between the loss of energy and energy conversion during the interaction of an ISW with an obstacle. The maximum wave energy loss obtained by eliminating the effect of the tailed wave generated during wave generation and considering the energy conversion is approximately 5%–10% lower than that obtained with traditional methods. Additionally, the mode-2 ISW was detected during the wave-topography interaction, and its velocity profiles in the vertical direction were analyzed, which may be one of the reasons for the accelerated energy dissipation in the system.

Mixing Efficiency for Breaking Internal Solitary Waves

AbstractWe propose a semi‐analytic approach to estimate mixing induced by internal solitary waves (ISWs) breaking over a sloping boundary. The theoretical framework we develop describes the energetics of a stratified fluid flow during the interaction of ISWs with a slope. In particular, through both Ozmidov and Thorpe lengthscales we derive a heuristic expression for mixing efficiency, valid for plunging and plunging‐collapsing breakers. On the other hand, we perform laboratory experiments that also provide mixing efficiency by estimating both changes of the background potential energy and the incident and reflected ISWs energy. We then compare those results with the ones derived by our theoretical model, obtaining a power law that relates the two quantities. This function allows to estimate mixing efficiency when the change in the background potential energy due to the ISWs breaking is unknown. We finally successfully apply our model to estimate the mixing efficiency under real field conditions.

Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin–Ono equation

The interaction of a solitary wave with a long background periodic wave in a deep ocean is studied within the framework of the rotation modified Benjamin–Ono equation. Using a multiple scales analysis, we find stationary and nonstationary solutions for a Benjamin–Ono soliton trapped within a long sinusoidal wave. We show that the radiation losses experienced by the soliton and caused by the Earth’s rotation can be compensated by energy pumping from the background wave. However, the feedback of the soliton on the background wave eventually leads to the destruction of the coherent structure and energy dispersion in a quasi-random wave field. Estimates of the characteristic parameters of the soliton dynamics are presented for real oceanic conditions.

Frontal collision of two nonlinear internal solitary waves in a stratified fluid

Head-on collision of two internal solitary waves (ISWs) in a two-layer inviscid fluid with fully nonlinear free-surface (FS) condition is investigated numerically in this paper. The collision process of and nonlinear interaction of internal solitary waves is studied based on nonlinear potential flow theory and a series of numerical simulations are conducted using a multi-domain boundary element method (MDBEM). The numerical model is validated by experiment for the simulation of ISWs propagating. The computation results show that the collision of ISWs is the asymmetric and nonlinear process in which the rundown motion causes the interface displacement penetrates the interface. The collision leaves imprints on small dispersive trailing waves which accounts for the attenuation with each departing ISW tilting slightly backward with respect to the direction of its propagation. In addition, the characteristic of collision process including run up, residence time, surface wave feature is discussed. During the collision, the wave spends more time falling than rising for all cases and the residence time is very long for waves of small amplitude, large depth ratios and density ratios. Considering the free surface of the top layer whether or not makes contributions to the run up and the residence time is larger if the top boundary is free surface.

The role of Internal Solitary Waves on deep-water sedimentary processes: the case of up-slope migrating sediment waves off the Messina Strait.

Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.

Characteristics of Mach effect induced by oblique wave-wave interactions of internal solitary waves in ocean

The Mach effect induced by the oblique wave-wave interactions of internal solitary waves is a special phenomenon of the ocean and is also the main reason of generating a large amplitude internal solitary wave, while they can cause it damage and even crash as the ocean engineering structures or underwater vehicles encounter the internal solitary wave with a large ampiltude in the ocean. In order to simulate the oblique interaction of internal solitary waves in the thermocline marine environment and control the Mach effect in the laboratory, two vertical bottomless barrels are placed in the fresh/saline water’s two-layer fluid. So the mixed fresh/saline water region is called the density thermocline of the marine. Keeping exchange of water under the barrel’s bottoms is to facilitate the formation of the mixed region height difference in the inner and outer parts of barrels. And then remove the two barrels smoothly and quickly, so that the mixed fresh/saline water region’s gravitational collapse motion can be made use of to generate two rows of internal solitary waves. They will occur the oblique wave-wave interaction in their propagating intersection area. The experimental results showed that two rows of solitary wave oblique interaction depends on the stratification environment, the distance between the two barrels and the amplitude and phase of two solitary waves. It has been vertfied that the above method can effectively control the generation of Mach effect in the stratified fluid tank. Further analysis showed that the Mach effect induced by the oblique interaction of internal solitary waves will lead to remarkably increasing amplitude in correspondence with its raising propagation velocity, whose direction is controlled by the amplitude difference between two internal solitary waves, and the greater amplitude difference will bring on the larger Mach effect’s critical angle. Through testing the theoretical models including KdV’, BO’ and MCC’s equations to compare with the experimental results , the adaptability of the Mach effect to the nonlinear theoretical models is verified by experiments.

Transformation of internal solitary waves at the "deep" and "shallow" shelf: satellite observations and laboratory experiment

Abstract. An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the "deep" and the "shallow" shelf respectively. The first one provides the generation of the secondary periodic short internal waves – "runaway" edge waves – due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.

Fluid circulation and seepage in lake sediment due to propagating and trapped internal waves

It has long been known that surface gravity waves induce significant seepage through the porous layer found at the lake bottom. Away from coastal regions, however, the pressure signature of surface waves at the lake bottom is weak. We consider fully nonlinear internal gravity waves, whose long wavelength and slow motion implies a sustained and strong pressure perturbation even in the deep regions of the lake. We argue that internal waves can induce significant seepage through the sediment layer, in regions where surface gravity waves have negligible impact. The pressure profile at the fluid–porous layer interface is computed from the “exact” Dubreil‐Jacotin‐Long theory, giving a reliable profile even for large waves. This profile is used in conjunction with Darcy's law to compute the seepage within the porous region. We find that the geometric distribution of seepage is strongly controlled by both the ratio of porous media thickness to the horizontal length of the pressure perturbation, and the bottom topography, when it is present. Based on work on the interaction of internal solitary waves with the bottom boundary layer, we develop a model to account for the changes in permeability due to wave‐induced instabilities in the bottom boundary layer and enhanced benthic turbulence. This turbulence acts to unplug the pores near the surface by lifting the detritus that clogs them. The resulting changes in permeability significantly enhance exchange between the free fluid and the porous medium on the downstream side of the wave.

NONLINEAR OBLIQUE INTERACTION OF LARGE AMPLITUDE INTERNAL SOLITARY WAVES

Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including 'freak waves'). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called "resonant interaction† because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction ("stem† wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equation (ex. Tsuji and Oikawa, 2006) suggest also qualitatively similar result. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonant behavior is found or not. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude. In contrast, a "stem" was not found to occur when the incident wave angle was more than the critical angle, which has been demonstrated in the previous studies.

Large Amplitude Internal Solitary Waves due to Solitary Resonance

To clarify the resonance of fully-nonlinear internal solitary waves which is one of the reasons for the occurrence of large amplitude internal waves, fully-nonlinear and strongly-dispersive internal wave equation model was applied, which attempted to investigate interaction of internal solitary waves in a two-dimensional plane. The 3rd order theoretical solutions for internal waves in a two-layer system was used for the initial conditions and progress of internal solitary wave was confirmed. Seven different incident wave angles were given, in which 'stem' was confirmed to appear when incident wave angle is less than critical angle. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude.

Amplitude decay and energy dissipation due to the interaction of internal solitary waves with a triangular obstacle in a two-layer fluid system: the blockage parameter

Experiments were carried out in a wave flume to examine the propagation of depression-type internal solitary waves (ISWs) over a submerged triangular-shaped obstacle. We observed the distortion and breaking of the ISW depression in a two-layer stratified fluid system as induced by the obstacle on the bottom. Physical factors, such as the amplitude of the wave, the thickness of the two layers, and the height of the submerged obstacle were utilized in our analysis of the wave–obstacle interaction. Wave breaking was determined in relation to input parameters arranged before the experimental runs. A classification scheme based on the blockage parameter ζ was proposed. The various degrees of ISW-obstacle interaction were visually classified with three schematic forms (ζ < 0.55 for a weak encounter; 0.55 < ζ < 0.7 for a moderate encounter; and 0.7 < ζ for wave breaking). Furthermore, the reflection and transmission coefficients were utilized to explore the resultant influence on changes in amplitude and energy of an ISW. The wave characteristics (e.g., amplitude-based wave reflection, energy-based reflection, amplitude-based transmission, and energy-based transmission) during the wave–obstacle interaction showed an approximately linear relation with the blockage parameter. Influenced by the submarine obstacle, the transmitted waves were found to always consist of a leading pulse (solitary wave) followed by a dispersive wave train. Moreover, due to bottom friction the energy budget of the leading pulse was reduced by a factor of at least 5% which could approach 50% in cases with strong breaking.

Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth

Oblique interaction of internal solitary waves in a two-layer fluid system with infinite depth is studied. Two-dimensional Benjamin–Ono (BO) equation is solved numerically to investigate the strong interactions of the non-linear long waves whose propagation directions are very close to each other. Computations of time development are performed for two initial settings: the first one is superposition of two BO solitons with the same amplitude and with different propagation directions, and the second one is an oblique reflection of a BO soliton at a vertical wall. It is observed that the Mach reflection does occur for small incident angles and for some incident angles very large stem waves are generated.

Intermodal interaction of internal solitary waves

Intermodal interaction of internal solitary waves

Intermodal interaction of internal solitary waves

Interaction of internal solitary waves of different modes in an incompressible fluid with an exponential stratification in density is considered. Two such waves are considered. These waves may be going in the same direction or in opposite directions. The analysis shows that the interaction produces two pairs of waves, whose mode indices are the difference and the sum of those of the original waves, respectively. Each pair consists of a right-going wave and a left-going one, and a part that vanishes eventually everywhere. Higher-order terms affecting interaction are briefly discussed. The interaction of more than two waves can be dealt with pair by pair.

Two-Dimensional Interaction of Internal Solitary Waves in a Two-Layer Fluid

Two-dimensional interaction of internal solitary waves is studied for a two-layer fluid with a thickness ratio close to a certain critical one depending on the density ratio. It is described by a Modified Kadomtsev-Petviashvili (MKP) equation, provided the propagation directions of the waves are close to each other. The MKP equation is investigated numerically and it is found that the interaction almost satisfying the condition of soliton resonance occurs when the wave amplitudes are small. The interaction is qualitatively similar to the soliton resonance in the Kadomtsev-Petviashvili (KP) equation except that a deformation of the newly generated waves and a radiation can be seen.