International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 9, Pages 499-515
Effects of diffraction and radiation on a submerged sphere
Department of Engineering Mathematics, Dalhousie University, P.O. Box 1000, Nova Scotia, Halifax B3J 2X4, Canada
Received 20 July 2001
Copyright © 2001 Matiur Rahman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper deals with an investigation of the effects of
diffraction and radiation on a submerged sphere in water of finite
depth . We assume that the fluid is homogeneous, inviscid, and
incompressible, and the fluid motion is irrotational. In real
situations, the submerged sphere will experience six degrees of
freedom (i.e., motions); three translational and three rotational.
In this paper, however, we consider a very idealized
situation because of the complex nature of the physical problem.
Two important motions, namely, the surge (horizontal oscillations)
and the heave (vertical oscillations) motions are studied. Our
attention is mainly focused on the hydrodynamic coefficients of
these motions. The crux of the problem lies entirely on the
determination of these coefficients which are inherently related
to the determination of the motions of the submerged sphere in
regular waves. This type of problem is usually solved by using
potential theory, and mathematically, we look for the solution of
a velocity potential which satisfies Laplace's equation along with
the free surface, body surface, and bottom boundary conditions in
conjunction with a radiation condition. This boundary value
problem, in fact, consists of two separate problems: (a)
diffraction problem and (b) radiation problem.