On interfacial solitary waves over slowly varying topography

Abstract

The propagation of long, weakly nonlinear interfacial waves in a two-layer fluid of slowly varying depth is studied. The governing equations are formulated to include cubic nonlinearity, which dominates quadratic nonlinearity in some parametric neighbourhood of equal layer depths. Numerical solutions are obtained for an initial profile corresponding to either a single solitary wave or a rank-ordered pair of such waves incident in a monotonic transition between two regions of constant depth. The numerical solutions, supplemented by inverse-scattering theory, are used to investigate the change of polarity of the incident waves as they pass through a ‘turning point’ of approximately equal layer depths. Our results exhibit significant differences from those reported by Knickerbocker & Newell (1980), which were based on a model equation. In particular, we find that more than one wave of reversed polarity may emerge.