Solitary Wave Evolution Over a Gradual Slope with Turbulent Friction

Abstract

A solitary wave of amplitude a evolving in water of depth d over a bottom of gradual slope δ and turbulent friction coefficient Cf is found to have the asymptotic (as d ?0) relative amplitude a/d = α1 = 15α/4Cf α1<αb where αb, is the relative amplitude above which breaking occurs. It is argued that an initially sinusoidal wave of sufficiently small amplitude evolves over a shoaling bottom into a periodic sequence of solitary waves with relative amplitude α1. This prediction is supported by observations (Wells, 1978) of the evolution of swell over mud flats.