On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions
TL;DR: In this article, the authors show how trains of nonlinear, dispersive waves can be produced by allowing a region of mixed fluid, with a potential energy greater than its surroundings, to collapse towards its equilibrium state.
Abstract: The paper shows how trains of nonlinear, dispersive waves can be produced by allowing a region of mixed fluid, with a potential energy greater than its surroundings, to collapse towards its equilibrium state. The number of waves and their amplitude depend on the properties of the mixed region and of the ambient stratification. Three different geometrical configurations have been chosen and while each gives qualitatively the same results the form taken by the generated waves and the final equilibrium shape of the mixed region depend critically on these geometrical factors. The internal waves produced by this mechanism are related to waves produced in natural systems and it is shown that the observations support at least one possible explanation for those found in the oceans and planetary atmospheres.
Citations
More filters
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.
Abstract: Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides 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. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.
676 citations
Cites background from "On the formation of nonlinear inter..."
...In some cases the mixed fluid evolved into, or forced, what appeared to be second-mode solitary waves (c.f., Davis & Acrivos 1967, Maxworthy 1980, Vlasenko & Hutter 2001)....
[...]
...F or p er so na l u se o nl y. Davis & Acrivos (1967), Maxworthy (1980), and Stamp & Jacka (1996) considered mode-two waves produced by the gravitational collapse of mixed fluid into a stratified layer bounded by deep homogeneous layers....
[...]
Book•
[...]
TL;DR: The Turbulent Ocean as discussed by the authors describes the principal dynamic processes that control the distribution of turbulence, its dissipation of kinetic energy and its effects on the dispersion of properties such as heat, salinity, and dissolved or suspended matter in the deep ocean, the shallow coastal and the continental shelf seas.
Abstract: The subject of ocean turbulence is in a state of discovery and development with many intellectual challenges. This book describes the principal dynamic processes that control the distribution of turbulence, its dissipation of kinetic energy and its effects on the dispersion of properties such as heat, salinity, and dissolved or suspended matter in the deep ocean, the shallow coastal and the continental shelf seas. It focuses on the measurement of turbulence, and the consequences of turbulent motion in the oceanic boundary layers at the sea surface and near the seabed. Processes are illustrated by examples of laboratory experiments and field observations. The Turbulent Ocean provides an excellent resource for senior undergraduate and graduate courses, as well as an introduction and general overview for researchers. It will be of interest to all those involved in the study of fluid motion, in particular geophysical fluid mechanics, meteorology and the dynamics of lakes.
380 citations
334 citations
TL;DR: In this paper, the authors have clarified the mechanisms whereby a train of solitary waves can be generated by the barotropic tidal flow of a stratified fluid over a three-dimensional obstacle.
Abstract: Using a simple laboratory model we believe that we have clarified the mechanisms whereby a train of solitary waves can be generated by the barotropic tidal flow of a stratified fluid over a three-dimensional obstacle. As the tidal flow reaches critical value of the internal Froude number a downstream depression is formed in the mixed layer. When the tide slackens and turns, this depression moves upstream and evolves into a sequence of solitary waves. Under some circumstances the depression becomes turbulent, and intense mixing takes place. In this case it is also the collapse of the mixed region that generates solitary waves which mainly propagate upstream. Available field data are consistent with this explanation, and we can estimate the number of waves formed using existing theory.
302 citations
TL;DR: In this paper, the experiments on solitons in plasmas performed during the period 1970 to 1982 are reviewed and suggested suggestions for future experiments are presented, as well as a review of the results.
Abstract: The experiments on solitons in plasmas performed during the period 1970 to 1982 are reviewed. Suggestions for future experiments are presented.
267 citations
References
More filters
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.
Abstract: This paper presents a general theoretical treatment of a new class of long stationary waves with finite amplitude. As the property in common amongst physical systems capable of manifesting these waves, the density of the (incompressible) fluid varies only within a layer whose thickness h is much smaller than the total depth, and it is h rather than the total depth that must be considered as the fundamental scale against which wave amplitude and length are to be measured. Internal-wave motions supported by the oceanic thermocline appear to be the most promising field of practical application for the theory, although applications to atmospheric studies are also a possibility.The waves in question differ in important respects from long waves of more familiar kinds, and in § 1 their character is discussed on the basis of a comparison with solitary-wave and cnoidal-wave theories on customary lines, such as apply to internal waves in fluids of limited depth. A summary of some simple experiments is included at the end of § 1. Then, in § 2, the comparatively easy example of two-fluid systems is examined, again to illustrate principles and to prepare the way for the main analysis in § 3. This proceeds to a second stage of approximation in powers of wave amplitude, and its leading result is an equation (3·51) determining, for arbitrary specifications of the density distribution, the form of the streamlines in the layer of heterogeneous fluid. Periodic solutions of this equation are obtained, and their properties are discussed with regard to the interpretation of internal bores and wave-resistance phenomena. Solutions representing solitary waves are then obtained in the form
\[
f(x) = a\lambda^2/(x^2+\lambda^2),
\]
where xis the horizontal co-ordinate and where aΛ = O(h2). (The latter relation between wave amplitude and length scale contrasts with the customary one, aΛ2 = O(h3)). The main analysis is developed with particular reference to systems in which the heterogeneous layer lies on a rigid horizontal bottom below an infinite expanse of homogeneous fluid; but in § 4 ways are given to apply the results to various other systems, including ones in which the heterogeneous layer is uppermost and is bounded by a free surface. Finally, in §5, three specific examples are treated: the density variation with depth is taken, respectively, to have a discontinuous, an exponential and a ‘tanh’ profile.
979 citations
875 citations
TL;DR: By using nonlinear perturbation method, a time-dependent equation is derived which governs internal waves in stratified fluids of great depth as discussed by the authors, and the resultant equation takes the following form :
Abstract: By using nonlinear perturbation method a time-dependent equation is derived which governs internal waves in stratified fluids of great depth. The resultant equation takes the following form :
749 citations
TL;DR: In this paper, the problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes.
Abstract: The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.
407 citations