Book ChapterDOI
Internal Solitary Waves
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In this article, the basic theory of internal solitary waves is developed, with the main emphasis on environmental situations, such as the many occurrences of such waves in shallow coastal seas and in the atmospheric boundary layer.Abstract:
The basic theory of internal solitary waves is developed, with the main emphasis on environmental situations, such as the many occurrences of such waves in shallow coastal seas and in the atmospheric boundary layer. Commencing with the equations of motion for an inviscid, incompressible density-stratified fluid, we describe asymptotic reductions to model long-wave equations, such as the well-known Korteweg-de Vries equation. We then describe various solitary wave solutions, and propose a variable-coefficient extended Korteweg-de Vries equations as an appropriate evolution equation to describe internal solitary waves in environmental situations, when the effects of a variable background and dissipation need to be taken into account.read more
Citations
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Journal ArticleDOI
Long Nonlinear Internal Waves
TL;DR: In this paper, an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example.
Journal ArticleDOI
Long nonlinear surface and internal gravity waves in a rotating ocean
TL;DR: In this paper, nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed and attention is focused upon guided waves long compared to the ocean depth.
Journal ArticleDOI
Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves
TL;DR: In this paper, the variation of the solitary wave parameters can be described analytically through an asymptotic description as a slowly varying solitary wave, which possesses a soliton-like form with varying amplitude and phase.
Journal ArticleDOI
Unsteady undular bores in fully nonlinear shallow-water theory
TL;DR: In this article, the authors considered unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully non-linear dispersive terms.
Journal ArticleDOI
Large fully nonlinear internal solitary waves: The effect of background current
Marek Stastna,Kevin G. Lamb +1 more
TL;DR: In this paper, the amplitude of the largest non-breaking wave in a shallow, stratified ocean has been investigated and it was shown that the maximum wave amplitude is given by one of three possibilities: the onset of wave breaking, the conjugate flow amplitude or a failure of the wave calculating algorithm to converge.
References
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Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Journal ArticleDOI
Internal waves of permanent form in fluids of great depth
TL;DR: In this paper, a general theoretical treatment of a new class of long stationary waves with finite amplitude is presented, which differ in important respects from long waves of more familiar kinds, and their character is discussed on the basis of a comparison with solitary-wave and cnoidal-wave theories on customary lines.
Journal ArticleDOI
Solitary internal waves in deep water
Russ E. Davis,Andreas Acrivos +1 more
TL;DR: In this article, a new type of solitary wave motion in incompressible fluids of non-uniform density has been investigated experimentally and theoretically, where a fluid is stratified in such a manner that there are two layers of different density joined by a thin region in which the density varies continuously, and the wave propagates along the density gradient region without change of shape.