Nonlinear Dynamics of Three-dimensional Solitary Waves

Nonlinear Dynamics of Three-dimensional Solitary Waves
Author: Yeunwoo Cho
Publisher:
Total Pages: 108
Release: 2010
Genre:
ISBN:

In problems of dispersive wave propagation governed by two distinct restoring-force mechanisms, the phase speed of linear sinusoidal wavetrains may feature a minimum, cmin, at non-zero wavenumber, kmin. Examples include waves on the surface of a liquid in the presence of both gravity and surface tension, flexural waves on a floating ice sheet, in which case capillarity is replaced by the flexural rigidity of the ice, and internal gravity waves in layered flows in the presence of interfacial tension. The focus here is on deep-water gravity-capillary waves, where cmin = 23 cm/s with corresponding wavelength Amin = 27r/kmin = 1.71 cm. In this instance, ignoring viscous dissipation, cmin is known to be the bifurcation point of two-dimensional (plane) and three-dimensional (fully localized) solitary waves, often referred to as "lumps"; these are nonlinear disturbances that propagate at speeds below cmin without change of shape owing to a perfect balance between the opposing effects of wave dispersion and nonlinear steepening. Moreover, Cmin is a critical forcing speed, as the linear inviscid response to external forcing moving at Cmin grows unbounded in time, and nonlinear effects as well as viscous dissipation are expected to play important parts near this resonance. In the present thesis, various aspects of the dynamics of gravity-capillary lumps are investigated theoretically. Specifically, it is shown that steep gravity-capillary lumps of depression can propagate stably and they are prominent nonlinear features of the forced response near resonant conditions, in agreement with companion experiment for the generation of gravity-capillary lumps on deep water. These findings are relevant to the generation of ripples by wind and to the wave drag associated with the motion of small bodies on a free surface.

Nonlinear Ocean Dynamics

Nonlinear Ocean Dynamics
Author: Maged Marghany
Publisher: Elsevier
Total Pages: 464
Release: 2021-02-09
Genre: Science
ISBN: 0128209259

Nonlinear Ocean Dynamics: Synthetic Aperture Radar delivers the critical tools needed to understand the latest technology surrounding the radar imaging of nonlinear waves, particularly microwave radar, as a main source to understand, analyze and apply concepts in the field of ocean dynamic surface. Filling the gap between modern physics quantum theory and applications of radar imaging of ocean dynamic surface, this reference is packed with technical details associated with the potentiality of synthetic aperture radar (SAR). The book also includes key methods needed to extract the value-added information necessary, such as wave spectra energy, current pattern velocity, internal waves, and more. This book also reveals novel speculation of a shallow coastal front: named as Quantized Marghany's Front. Rounding out with practical simulations of 4-D wave-current interaction patterns using using radar images, the book brings an effective new source of technology and applications for today’s coastal scientists and engineers. Solves specific problems surrounding the nonlinearity of ocean surface dynamics in synthetic aperture radar data Helps develop new algorithms for retrieving ocean wave spectra and ocean current movements from synthetic aperture radar Includes over 100 equations that illustrate how to follow examples in the book

Nonlinear Internal Waves in Lakes

Nonlinear Internal Waves in Lakes
Author: Kolumban Hutter
Publisher: Springer Science & Business Media
Total Pages: 292
Release: 2011-11-25
Genre: Science
ISBN: 3642234380

Internal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of ‘quiescent’ water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (

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.

Dynamics of Internal Gravity Waves in the Ocean

Dynamics of Internal Gravity Waves in the Ocean
Author: Yu.Z. Miropol'sky
Publisher: Springer Science & Business Media
Total Pages: 750
Release: 2001-04-30
Genre: Science
ISBN: 9780792369356

This monograph creates a systematic interpretation of the theoretical and the most actual experimental aspects of the internal wave dynamics in the ocean. Firstly, it draws attention to the important physical effects from an oceanographical point of view which are presented in mathematical descriptions. Secondly, the book serves as an introduction to the range of modern ideas and the methods in the study of wave processes in dispersive media. The book is meant for specialists in physics of the ocean, oceanography, geophysics, hydroacoustics.

Three-Dimensional Models of Marine and Estuarine Dynamics

Three-Dimensional Models of Marine and Estuarine Dynamics
Author: J.C.J. Nihoul
Publisher: Elsevier
Total Pages: 643
Release: 1987-05-01
Genre: Science
ISBN: 008087083X

These proceedings represent the most recent and complete state of the art review of three-dimensional models of the modern generation for the study of marine hydrodynamics and management of the marine system. The book is well illustrated by application to well-documented case studies.

Nonlinear Water Waves

Nonlinear Water Waves
Author: David Henry
Publisher: Springer Nature
Total Pages: 218
Release: 2019-11-27
Genre: Mathematics
ISBN: 3030335364

The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume. Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.