Numerical Simulations of Internal Solitary and Solitary-like Waves

Numerical Simulations of Internal Solitary and Solitary-like Waves
Author: Chengzhu Xu
Publisher:
Total Pages: 149
Release: 2019
Genre: Fluid dynamics
ISBN:

Internal solitary and solitary-like waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a varying background environment, they may change their form and possibly become unstable. In this thesis, we study ISWs using high-resolution direct numerical simulations and address three major topics: the interaction of ISWs with short waves, the onset of shear instability in ISWs, and the dynamics of ISWs in a shear background current induced by basin-scale standing internal waves. The first topic examines the behavior of short internal waves as they propagate through large-amplitude ISWs. A key finding is that for waves that are short in comparison to the ISW width, the interaction leads to an almost complete destruction of the short waves, but that longer waves are able to maintain their structure after the interaction. The destruction of short waves occurs primarily due to the velocity shear induced by the ISW, which alters the vertical structure of the short waves so that significant wave activity is found only on the upstream side of the ISW crest (i.e. the deformed pycnocline). These results suggest that through the interaction with waves of relatively smaller length scale, ISWs can provide a means to decrease the power observed in the short-wave band in the coastal ocean. The second topic focuses on the onset and growth of shear instability in ISWs, which is particularly important for the diapycnal mixing in open waters. The complexity of instability onset in ISWs is due to the finite length and the non-parallel structure of the wave-induced high-shear region. We examine large-amplitude ISWs with a flat crest and show that, depending on the ratio of the length of high shear region and the width of the wave, there are cases in which instability can occur spontaneously, cases in which its onset is Reynolds number dependent, and cases in which instability does not occur spontaneously but must be triggered by small, but finite amplitude noise. The amplitude of the noise has a crucial influence on the instability growth, regardless of its spatial structure. In the final topic we study the effect of a shear background current on the dynamics of ISWs by investigating the interaction of ISWs with basin-scale standing internal waves. The ISWs are generated using a lock-release mechanism, while the seiches are created using a tilted tank suddenly returned to the upright position, both of which are readily realizable in a laboratory. In most cases, the wave forms of ISWs in the simulations match those described by the fully nonlinear theory, implying that in laboratory experiments ISWs propagating in a shear background current can be generated in a similar manner. In some circumstances, however, the presence of a shear background current prevents the formation of ISWs, but enables the formation of a finite amplitude dispersive wave train, even when the pycnocline center is not close to the mid-depth.

Environmental Stratified Flows

Environmental Stratified Flows
Author: Roger Grimshaw
Publisher: Springer Science & Business Media
Total Pages: 286
Release: 2006-04-11
Genre: Science
ISBN: 0306480247

The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.

Numerical Simulation of Nonlinear Internal Solitary Wave Interactions with Submarine Topographic Features

Numerical Simulation of Nonlinear Internal Solitary Wave Interactions with Submarine Topographic Features
Author: Michael Peter Lee
Publisher:
Total Pages: 455
Release: 2011
Genre: Internal waves
ISBN:

Approximately 120 computer simulations were conducted to evaluate how a mode-1-type internal wave would interaction with a variety of submarine topographic (physiographic) obstacles likely to be found in a marine setting. A total of seven obstacle geometries were selected for evaluation - shelf, slope-shelf, extended slope, short-slope, reverse-shelf, a single (isolated) rectangular obstacle, and a single triangular obstacle. Internal waves of `depression' as well as `elevation' were formed using a two-layered, stratified numerical model based on the Navier-Stokes and continuity equations. The governing equations assumed Boussinesq conditions. Output data from the FORTRAN-based computer code were post-processed using MATLAB-based computer programs that calculated internal wave amplitudes and energies. These data were compared to published data associated with experimental wave tank studies and found generally to be in good agreement. Data from the numerical simulation trials were also used to generate figures illustrating various hydrodynamic features (pycnocline, streamlines, and velocity vectors) of an internal wave as it forms as well as when it interacts with different types of obstacle geometries. The types of features and processes observed included the formation of Kelvin-Helmholtz or K-H-like vortices and various stages of the classically-recognized wave-breaking progression ("wash-down," "breaking," "bore," and "surge"). When considering a stratified fluid system, it was confirmed that internal wave characteristics are influenced in large measure by the relative depths of the two fluids defining the system as well as the effects of viscous decay (damping). It was also confirmed that the nature of the interaction between an internal wave and a topographic obstacle is influenced by the magnitude of either the nonlinear parameter or the blocking parameter. The numerical simulation trials also allowed for the interrogation of the modeling domain to determine the nature of the stability conditions (static vs. dynamic) in time and space. In this regard, evaluation of both the Richardson number and the normalized density gradient provided additional insights into the hydrodynamics of the system when topographic obstacles are present. Three instability states were evaluated: K-H, buoyant, and static. This research contributes to a basic understanding of internal wave phenomena and includes some general conclusions regarding the effects of obstacle geometry on internal wave behavior and properties.

Numerical Simulations of Nonlinear Internal Waves in the South China Sea

Numerical Simulations of Nonlinear Internal Waves in the South China Sea
Author: Zhonghua Zhang
Publisher:
Total Pages:
Release: 2010
Genre:
ISBN:

Field observations and satellite imagery have demonstrated the ubiquitous nature of internal waves, and substantial evidence indicates that they play a significant role in nutrient transport, energy distribution and mixing throughout the world's oceans. As a result, internal waves have attracted a great deal of interest in the past few decades. However, because of the complex nature of internal waves, particularly in regard to their nonlinear and nonhydrostatic characteristics, basic properties of internal waves still lack satisfactory explanation, including how they are generated, how they propagate, and how they dissipate their energy in the open ocean and on continental margins. To obtain a better understanding of internal waves, we use SUNTANS, a three-dimensional, unstructured-grid, nonhydrostatic Navier-Stokes code, to simulate internal waves in the South China Sea (SCS), where extremely large-amplitude internal waves have been observed. To capture the nonlinear features of internal waves, a total variation diminishing method has been developed to accurately solve the three-dimensional scalar transport equation with unstructured grids in SUNTANS. Taking advantage of this scheme, we employ both two- and three-dimensional numerical simulations with idealized and real bathymetry and perform detailed analyses of internal wave energetics and dynamics to understand how they are generated in the SCS and how they evolve into trains of weakly nonlinear solitary-like waves. The simulation results indicate that nonlinear internal waves in the SCS are generated by strong barotropic flow over complex topography at a ridge on the eastern edge of the Luzon Strait, which connects the eastern boundary of the SCS to the Pacific Ocean. Idealized two-dimensional simulations show that the internal Froude number over the topography, or the ratio of the barotropic currents to the first-mode internal wave speed, can be the most important parameter governing the generation with a strong effect both on the amplitude of the generated waves and the phase in the barotropic tide at which internal waves are generated. For low-Froude number generation, linear first-mode waves are always generated at the end of the ebb tide, and increasing the Froude number causes waves to be generated earlier given the flow is subcritical. However, because the internal Froude number in the SCS is small, the three-dimensional simulations with real topography and stratification indicate that the excursion parameter, which is the ratio of the tidal excursion to the topographic scale, is the most important parameter governing the generation mechanism. With small tidal excursion parameters in the SCS, the well-known A and B waves are both likely generated by the internal tide mechanism. The A waves evolve from the formation of diurnal internal tidal beams at critical topography along the eastern ridge of the two ridge-system in the southern portion of the Luzon Strait. The B waves, on the other hand, are generated due to the formation of internal tides resulting from semidiurnal barotropic currents along the eastern ridge in the northern portion of the Luzon Strait. An analysis of the energetics indicates that half of the baroclinic or internal tidal energy dissipates locally over the ridge within the Strait, while the other half radiates away from the generation site and into the SCS basin. As the waves propagate across the SCS basin, they develop into trains of rank-ordered solitary-like internal waves under the effects of nonlinear steepening and nonhydrostatic dispersion. Because it employs the nonhydrostatic pressure, the SUNTANS model accurately captures these effects as well as the complex processes of wave diffraction, refraction, and wave-wave interaction on the continental shelf at the western edge of the SCS.

Two Dimensional Acoustic Propagation Through Oceanic Internal Solitary Waves

Two Dimensional Acoustic Propagation Through Oceanic Internal Solitary Waves
Author:
Publisher:
Total Pages: 65
Release: 2006
Genre: Hydrodynamics
ISBN:

Internal solitary waves, or solitons, are often generated in coastal or continental shelf regions when tidal currents advect stratified water over bathymetric relief, creating an internal tide which non-linearly evolves into one or more solitons. A major consequence of solitons in a stratified environment is the vertical displacement of water parcels which can lead to sound speed variability of order 10m/s with spatial scales of order 100 meters and timescales of order minutes. Thus significant variations in sonar performance on both surface based ships and submarines can be expected. An understanding into the nature of acoustic propagation through these waves is vital for future development of sonar prediction systems. This research investigates acoustic normal mode propagation through solitons using a 2D parabolic equation simulation and weak acoustic scattering theory whose primary physics is a single scatter Bragg mechanism. To simplify the theory, a Gaussian soliton model is developed that compares favorably to the results from a traditional sech2 soliton model. The theory of sound through a Gaussian soliton was then tested against the numerical simulation under conditions of various acoustic frequency, source depths, soliton position relative to the source and soliton number. The theoretical results compare favorably with numerical simulations at 75, 150 and 300-Hz. Higher frequencies need to be tested to determine the limits of the first order theory. Higher order theory will then be needed to address even higher frequencies and to deal with weakly excited modes. This research is the first step in moving from a state of observing acoustic propagation through solitons, to one of predicting it.

Solitary Waves in Fluids

Solitary Waves in Fluids
Author: R. Grimshaw
Publisher: WIT Press
Total Pages: 209
Release: 2007
Genre: Science
ISBN: 1845641574

Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.

Modelling Internal Solitary Waves and the Alternative Ostrovsky Equation

Modelling Internal Solitary Waves and the Alternative Ostrovsky Equation
Author: Yangxin He
Publisher:
Total Pages: 85
Release: 2014
Genre:
ISBN:

Internal solitary waves (ISWs) are commonly observed in the ocean, and they play important roles in many ways, such as transport of mass and various nutrients through propagation. The fluids considered in this thesis are assumed to be incompressible, inviscid, non-diffusive and to be weakly affected by the Earth's rotation. Comparisons of the evolution of an initial solitary wave predicted by a fully nonlinear model, IGW, and two weakly-nonlinear wave equations, the Ostrovsky equation and a new alternative Ostrovsky equation, are done. Resolution tests have been run for each of the models to confirm that the current choices of the spatial and time steps are appropriate. Then we have run three numerical simulations with varying initial wave amplitudes. The rigid-lid approximation has been used for all of the models. Stratification, flat bottom and water depth stay the same for all three simulations. In the simulation analysis, we use the results from the IGW as the standard. Both of the two weakly nonlinear models give fairly good predictions regarding the leading wave amplitudes, shapes of the wave train and the propagation speeds. However, the weakly nonlinear models over-predict the propagation speed of the leading solitary wave and that the alternative Ostrovsky equation gives the worst prediction. The difference between the two weakly nonlinear models decreases as the initial wave amplitude decreases.

Numerical Simulations of Shoaling Internal Solitary Waves of Elevation

Numerical Simulations of Shoaling Internal Solitary Waves of Elevation
Author: Chengzhu Xu
Publisher:
Total Pages: 75
Release: 2015
Genre:
ISBN:

We present high-resolution, two- and three-dimensional direct numerical simulations of laboratory-scale, fully nonlinear internal solitary waves of elevation shoaling onto and over a small-amplitude shelf. The three-dimensional, mapped coordinate, spectral collocation method used for the simulations allows for accurate modelling of both the shoaling waves and the bottom boundary layer. We focus on wave-induced instabilities during the shoaling and de-shoaling processes. The shoaling of the waves is characterized by the formation of a quasi-trapped core which undergoes a spatially growing stratified shear instability at its edge and a lobe-cleft instability in its nose. Both of these instabilities develop and three-dimensionalize concurrently, leading to strong bottom shear stress. During the de-shoaling process, the core breaks up and ejects fluid that forms a vortex-rich region near the down-sloping portion of the shelf. The flow in this region is highly turbulent and the bottom shear stress is extremely strong. Experiments with a corrugated bottom boundary are also performed. Boundary layer separation is found inside each of the corrugations during the wave's shoaling process. Our analyses suggest that all of these wave-induced instabilities can lead to enhanced turbulence in the water column and increased shear stress on the bottom boundary. Through the generation and evolution of these instabilities, the shoaling and de-shoaling cycles of internal solitary waves of elevation are likely to provide systematic mechanisms for material mixing and sediment resuspension. These mechanisms have significant environmental implications on the near-coastal regions of the world's oceans.