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

Forbes, L.K. and Hocking, G.C. (2006) An intrusion layer in stationary incompressible fluids Part 2: A solitary wave. European Journal of Applied Mathematics, 17 (05). pp. 577-595.

Preview

PDF - Published Version Download (213kB) | Preview

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.