On the breaking of water waves in a channel of arbitrarily varying depth and width

Abstract

By generalising an approach due to Gurtin, the Bernoulli equation is derived which governs the amplitude of an acceleration wave propagating on the surface of water at rest in a vertical walled channel of arbitrarily varying width and depth. Integration of the equation yields an explicit expression for the amplitude of the acceleration wave as a function of position, together with a simple criterion for determining when a wave will break. A special case of a non-breaking elevation wave propagating into deepening water is also found.