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.