WIT Press


On The Use Of Multipole Expansions To Approximate The Diffraction-radiation Wave Integrals

Price

Free (open access)

Paper DOI

10.2495/AFM000371

Volume

29

Pages

12

Published

2000

Size

1,095 kb

Author(s)

A.C. Mendes

Abstract

The object of this paper is to introduce a simplified manner to construct the Green function from the theory of linear gravity waves, as associated with forced oscillations of a submerged body near the surface of a deep fluid. The problem is formulated in the frequency domain, in terms of a velocity potential satisfying Laplace equation and adequate boundary conditions. The singular part of the solution, usually known as the Rankin potential, will be searched as the potential induced by a distribution of normal and tangential doublets. As to its regular part (Kelvin's potential), it will be assembled as a set of multipole expansions whose far-field exhibits the same behaviour as the source-dipole wave asymptotics. The singularity densities are afterwards determined by solving a linear system of algebraic equations, which gu

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