European Journal of Applied Mathematics



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


LAWRENCE K. FORBES a1 and GRAEME C. HOCKING a2
a1 School of Mathematics and Physics, University of Tasmania, Hobart 7001, Tasmania, Australia email: larry.forbes@utas.edu.au
a2 School of Mathematics and Statistics, Division of Science, Murdoch University, Murdoch 6150, Western Australia

Article author query
forbes lk   [Google Scholar] 
hocking gc   [Google Scholar] 
 

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.

(Received November 30 2005)
(Revised June 1 2006)