Hydrodynamics of a submerged oblate spheroid in finite water depth using the method of ultimate image singularities

Abstract

The present study provides a semi-analytical formulation for the diffraction problem by an immersed oblate spheroid in a liquid field of finite water depth. The method of image singularities in oblate geometry, allows the expansion of the velocity potential in series of auxiliary potentials and eventually, the derivation of analytical expressions for the hydrodynamic loads on the spheroid subjected to the action of regular surface waves. The axisymmetric placement of the spheroid is considered, namely, having its symmetrical axis perpendicular to the undisturbed free surface. The solution of the problem is based on the method of image singularities. Based on the same approach, a disc is simulated as an oblate spheroid. The whole process that has been performed for the spheroid, is performed for the disc as well. The favorable agreement between the results of the present method and existing data, ensures the accuracy and robustness of the proposed methodology.