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

Published online by Cambridge University Press:  08 February 2007

LAWRENCE K. FORBES  and
GRAEME C. HOCKING
LAWRENCE K. FORBES
Affiliation:
School of Mathematics and Physics, University of Tasmania, Hobart 7001, Tasmania, Australia email: larry.forbes@utas.edu.au
GRAEME C. HOCKING
Affiliation:
School of Mathematics and Statistics, Division of Science, Murdoch University, Murdoch 6150, Western Australia
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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.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 17 , Issue 5 , October 2006 , pp. 577 - 595
Copyright
2007 Cambridge University Press

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