Long nonlinear waves in stratified shear flows

Abstract

The governing equations for long weakly nonlinear waves in stratified shear flows are developed for general flows and density stratifications, with the Boussinesq approximation. Solitary wave solutions are found and their character investigated for several particular flows. Both solitary waves of elevation and depression are shown to exist, even for the same flow, depending on the Richardson number. The results suggest a qualitative difference in behaviour with Richardson number between solitary waves in flows with their maximum velocity within the fluid region and those in flows where the maximum velocity is attained at the boundary.