Solitary waves in stratified shear flows

An analysis is described of long, finite-amplitude internal waves in a stratified shear flow. Both regular and singular modes are considered with a nonlinear critical layer employed in the latter case. A three-layer model is used to develop the theory and closed-form expressions are obtained relating the phase speed to the Richardson number, the latter quantity being taken as O(1). The amplitude evolution equation is found to be either the Korteweg-de Vries equation or the Benjamin-Davis-Ono equation depending upon the distance of the more remote boundary from the edge of the shear layer.