Surface waves in deep water due to arbitrary periodic surface pressure

Abstract

The expressions for the velocity potential and the surface elevation are obtained for the three dimensional motion on surface waves generated by a surface pressure F(x, y)ei ωt, t>0, on the surface of a deep sea. The wave integrals are asymptotically evaluated for large distances and times by the method of stationary phase. By a direct passage to the limit t→∞, the steady state solution of the problem is evaluated in exact terms. The results are illustrated for a class of physically plansible pressure distributions on the surface. Some features of the wave motions are discussed.