Interaction of a train of regular waves with a rigid submerged ellipsoid

Abstract

This dissertation presents the practical and rigorous solution of the potential flow problem associated with the interaction of a train of regular surface gravity waves with a fixed rigid submerged half spheroid resting on the bottom. The linearized boundary-value problem is first formulated for a fixed semiellipsoid. The radiation problem of a rigid semi-ellipsoid oscillating in its various degrees of freedom, one degree at a time, in otherwise still water is also formulated simultaneously, so as to use its results to check the results of the first problem by Haskind's relations. In each case the solution is obtained by the Green's function approach. In this method the velocity potential is obtained by distributing unit wave sources over the surface of the object. The Green's function which represents the velocity potential for a unit wave source is chosen such that it satisfies all the conditions of the problem except the normal boundary condition on the surface of the object. When this condition is applied, the result is a Fredholm integral equation of the second kind which must be solved for the distribution function. In the numerical procedure the integral equation is replaced by a matrix equation which is solved on a digital computer. The numerical procedure is outlined in detail for the semiellipsoid and finally, numerical results are obtained for a half spheroid. ...