Evolution of Maximum Amplitude of Solitary Waves on Plane Beaches

Abstract

This paper presents a study of the transformation of solitary waves on plane beaches. A series of laboratory experiments is presented to describe the amplitude evolution of long waves; these experiments suggest that at least four different regions exist for the functional variation of the maximum amplitude, two regions before and two regions after breaking. Linear theory is used to provide an expression for the growth of solitary waves evolving first over constant depth and then over a sloping bottom, including reflection. This result is shown to be equivalent to the wave evolution expression known as Green's law, and the limitations of Green's original derivation are discussed. Other existing analytical results and certain empirical relationships are used to produce a formulation consistent with the laboratory data with the objective to model the entire process of solitary wave evolution.