Multipole expansions for wave diffraction and radiation in deep water

Abstract

A multipole expansion of the velocity potential is described for two- and three-dimensional wave diffraction and radiation problems. The velocity potential is expressed in terms of a series of multipole potentials. The wave terms and the local disturbance terms are represented by separated multipole potentials. Floating bodies and submerged bodies are treated in the same way. This approach differs from that of some other authors, who considered floating bodies and submerged bodies separately and derived entirely different multipoles. Semi-analytical solutions for a circular cylinder in two-dimensional motions are given. It is found that the local disturbance decays rapidly and steadily. The general application of the multipole expansion to arbitrary geometries is also presented, based on a method coupling multipoles to a boundary integral expression. Numerical results for several floating and submerged cylinders are presented.