The radiation and scattering of surface waves by a vertical circular cylinder in a channel

In this paper we consider the problems of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2d and depth H, and either extending from the bottom through the free surface or truncated so as to fill only part of the depth. These problems are solved, for arbitrary incident wavenumber k, by constructing appropriate multipoles for cylinders placed symmetrically in channels and then using the body boundary condition to derive a set of infinite systems of linear algebraic equations. For the general problems considered here, this method is superior to the more usual approach of using a set of image cylinders to model the channel walls, in particular the occurrence of modes other than the fundamental when kd > is accurately modelled and the correct form predicted for the far-field.