Fully nonlinear gravity-capillary solitary waves in a two-fluid system of finite depth

Document Type

Article

Publication Date

1-1-2002

Abstract

Large-amplitude waves at the interface between two laminar immisible inviscid streams of different densities and velocites, bounded together in a straight infinite channel are studied, when surface tension and gravity are both present. A long-wave approximation is used to develop a theory for fully nonlinear interfacial waves allowing amplitudes as large as the channel thickness. The result is a set of evolution equations for the interfacial shape and the velocity jump across it. Traveling waves of permanent form are studied and it is shown that solitary waves are possible for a range of physical parameters. All solitary waves can be expressed implicitly in terms of incomplete elliptic integrals of the third kind. When the upper layer has zero density, two explicit solitary-wave solutions have been found whose amplitudes are equal to h/4 or h/9, where 2h is the channel thickness. In the absence of gravity solitary waves are not possible but periodic ones are. Numerically constructed solitary waves are given for representative physical parameters.

Identifier

0036527884 (Scopus)

Publication Title

Journal of Engineering Mathematics

External Full Text Location

https://doi.org/10.1023/A:1016191131656

ISSN

00220833

First Page

321

Last Page

339

Issue

3-4

Volume

42

Grant

DMS-007228

Fund Ref

National Science Foundation

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