Hydrodynamics of submerged prolate spheroids advancing under waves: Wave diffraction with forward speed

The present study treats the hydrodynamic diffraction problem including forward speed of a fully submerged prolate spheroid advancing rectilinearly under a monochromatic wave field in water of infinite depth. The analytic method explicitly satisfies the Kelvin-Neumann boundary conditions. The formulation is based on employing spheroidal harmonics and expressing the ultimate image singularity system as a series of multipoles distributed along the major axis of the spheroid between the two foci. The outlined procedure results in compact closed-form expressions for the six Kirchhoff velocity potentials as well as for the various components of the hydrodynamic loads exerted on the rigid body moving under waves.