The interaction of large amplitude shallow-water waves with an ambient shear flow: non-critical flows

Abstract

This paper describes the behaviour of large amplitude, long gravity waves as they move over a horizontal bed into a region where the flow is steady but sheared in a vertical direction. A new class of exact solutions to the nonlinear hydraulic flow equations is derived. These solutions describe progressing waves and are sufficiently general to allow both the shape of the free surface at any instant and the shear profile of the undisturbed flow to be specified. The waves are examples of neutrally stable disturbances in the sense that they neither grow nor decay in amplitude, although, like simple waves on an unsheared flow, they can break.