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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 Hindawi Publishing Corporation. 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 d. 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.