ACCURATE NUMERICAL SOLUTIONS FOR NONLINEAR WAVES

Abstract

This paper describes numerical methods for the accurate solution of the nonlinear equations for water waves propagating on irrotational flow over a horizontal bed. Fourier approximation is used throughout. Firstly, the problem of waves propagating without change is considered, giving a set of nonlinear equations which may be conveniently solved by Newton's method. It is emphasized that the usual specification of water depth, wave height and wave period is not enough to solve the problem - an assumption as to wave speed or,mean current or mass flux must be included. Comparing results with previous theoretical and experimental results, good .agreement was obtained. In the second part un^ steady wave motion is examined, and a numerical method proposed for studying the evolution of unsteady disturbances. This is applied to the case of a solitary wave being reflected by a vertical wall. Close agreement with experimental results is obtained. In addition, design criteria for force and moment on the wall are suggested.