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

journal contribution
posted on 2023-05-16, 19:11 authored by Lawrence ForbesLawrence Forbes, Hocking, GC
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.

Funding

Australian Research Council

History

Publication title

European Journal of Applied Mathematics

Volume

17

Issue

5

Pagination

577-595

ISSN

0956-7925

Department/School

School of Natural Sciences

Publisher

Cambridge University Press

Place of publication

New York, USA

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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