منابع مشابه
Shallow water asymptotic models for the propagation of internal waves
We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camass...
متن کاملAn improved result for the full justification of asymptotic models for the propagation of internal waves
We consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The aim of this paper is to show that the full justification result of the model obtained by Duchêne, Israwi and Talhouk [SIAM J. Math. Anal., 47(1), 240–290], i...
متن کاملDecoupled and unidirectional asymptotic models for the propagation of internal waves
We study the relevance of various scalar equations, such as inviscid Burgers’, Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified with two approaches. The first method consists in approximating the flow with two decoupled, cou...
متن کاملAsymptotic Shallow Water Models for Internal Waves in a Two-Fluid System with a Free Surface
In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic wavelength of the system (shallow water regim...
متن کاملModels for Internal Waves in Deep Water
We study properties of solitary wave solutions of three evolution equations arising in the modeling of internal waves Our experiments indicate that broad classes of initial data resolve into solitary waves but also suggest that solitary waves do not interact exactly thus suggesting two of these equa tions are not integrable In the course of our numerical simulations interesting meta stable quas...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2008
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2008.02.003