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An intrusion layer in stationary incompressible fluids. II: A solitary wave. (English) Zbl 1124.76004

Summary: We study the propagation of a solitary wave in a horizontal fluid layer. 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.

MSC:

76B07 Free-surface potential flows for incompressible inviscid fluids
76B25 Solitary waves for incompressible inviscid fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
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