The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Properties of short-crested waves in water of finite depth

T. R. Marchanta1 and A. J. Robertsa1

a1 Department of Applied Mathematics, University of Adelaide G. P. O. Box 498, Adelaide, S. A. 5001, Australia.

Abstract

Short-crested waves are defined as propagating surface gravity waves which are doubly-periodic in the horizontal plane. Linearly, the short-crested wave system we consider occurs when two progressive wavetrains of equal amplitude and frequency are propagating at an angle to each other.

Solutions are calculated via a computer-generated perturbation expansion in wave steepness. Harmonic resonance affects the solutions but Padé approximants can be used to estimate wave properties such as maximum wave steepness, frequency, kinetic energy and potential energy.

The force exerted by waves being reflected by a seawall is also calculated. Our results for the maximum depth-integrated onshore wave force in the standing wave limit are compared with experiment. The maximum force exerted on a seawail occurs for a steep wave in shallow water incident at an oblique angle. Results are given for this maximum force.

(Received April 17 1986)

(Revised August 14 1986)