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An intrusion layer in stationary incompressible fluids Part 2: A solitary wave

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Forbes, LK and Hocking, GC (2007) An intrusion layer in stationary incompressible fluids Part 2: A solitary wave. European Journal of Applied Mathematics, 17 (5). pp. 577-595. ISSN 0956-7925

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Abstract

The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial
free surface above and below this intrusion layer, which is moving at constant speed through
a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented,
leading to a Korteweg–de Vries equation in which the two fluid interfaces move oppositely.
The intrusion layer solitary wave system thus forms a widening bulge that propagates without
change of form. These results are confirmed and extended by a fully nonlinear solution, in
which a boundary-integral formulation is used to solve the problem numerically. Limiting
profiles are approached, for which a corner forms at the crest of the solitary wave, on one or
both of the interfaces.

Item Type: Article
Journal or Publication Title: European Journal of Applied Mathematics
Publisher: Cambridge University Press
Page Range: pp. 577-595
ISSN: 0956-7925
Identification Number - DOI: 10.1017/S0956792506006711
Date Deposited: 07 Apr 2008 14:03
Last Modified: 18 Nov 2014 03:32
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