Hydrodynamic exciting forces on a submerged oblate spheroid in regular waves

It is the purpose of this study to provide the analytic solution for the hydrodynamic diffraction problem by stationary, submerged oblate spheroidal bodies subjected to harmonic incident waves in deep water. The analytical process employs the multipole expansion terms derived by Thorne [1] which describe the velocity potential at singular points within a fluid domain with free upper surface and infinite water depth. The multipole potentials are used to analytically formulate the diffraction component of the velocity potential which is initially described by relations involving both spherical and polar coordinates. The goal is to transform the constituent terms of the multipole potentials as well as the incident wave component in oblate spheroidal coordinates. To this end, the appropriate addition theorems are derived which recast Thorne's [1] formulas into infinite series of associated Legendre functions. (C) 2011 Elsevier Ltd. All rights reserved.