Finite-amplitude solitary waves at the interface between two homogeneous fluids

Abstract

Numerical solutions are presented for finite-amplitude interfacial waves. Only symmetric waves are calculated. Two cases are considered. In the first case the waves are free-surface solitary waves propagating on a basic flow with uniform vorticity. Large-amplitude waves of extreme form are calculated for a range of values of the basic vorticity. In the second case the waves are propagating on the interface between two homogeneous fluids of different densities, which are otherwise at rest. Again large-amplitude waves of extreme form are calculated for a range of values of the basic density ratio. In particular, in the Boussinesq limit when the density ratio is nearly unity, solitary waves of apparently unlimited amplitude can be found.