The effect of radiation velocity potentials on the drift force on a submerged sphere

Abstract

The effect of the motion of a submerged sphere on the horizontal drift force is investigated analytically. The multipole expansion method is used to derive analytical solutions for the diffraction and radiation velocity potentials in a series of associated Legendre functions. The second-order steady force is obtained by the far field method. The effect of all velocity potentials is taken into account in derivation of the horizontal drift force. The total contribution of the radiation velocity potential is minimal to the horizontal drift force if the center of mass is at a distance less than twenty percent of the radius from the center of the sphere. The effect of the radiation velocity potential in vicinity of the resonant frequency is augmented and may create a relatively large horizontal drift force.