Water waves produced by a cylindrical wave-maker

Abstract

The cylindrical wave-maker problem consists of finding the forced wave motion, with outgoing surface waves at infinity, generated by a harmonically oscillating circular cylindrical wave-maker immersed in water. The axisymmetric problem was first solved in 1929 by Sir Thomas Havelock, who ignored the effect of surface tension, and more recently, with the effect of surface tension included, by P.F. Rhodes-Robinson. The method used in both cases required a knowledge of certain expansion theorems (very complicated in the latter case) for the arbitrarily prescribed wave-maker velocity. In this thesis the solution of P.F. Rhodes-Robinson is obtained directly, using Green's theorem for harmonic functions and known expressions for the appropriate Green's function. Solutions are obtained for water of both finite and infinite depth. The Green's function for the non-axisymmetric problem with surface tension is also derived, and used to solve the general, non axisymmetric, cylindrical wave-maker problem.