Hydrodynamic interaction between a prolate spheroid and a sphere

The planar motion of a prolate spheroid around a sphere is investigated. Two sets of transformations of harmonics between the spherical co-ordinates and the prolate spheroidal ones are derived in terms of special functions. These transformations are employed to obtain the velocity potential for the two-body system of a moving prolate spheroid around a sphere by using the successive potential method, which is an extension of the sphere theorem. From the velocity potential, exact analytical expressions of added masses are thus obtained and adopted to determine the hydrodynamic interaction between these two bodies. The dynamical behaviour of the two-body system is discussed numerically for some typical situations. Numerical results demonstrate that the presence of a second body has an effect on the planar motion of the prolate spheroid, and the three-dimensional effect is feebler than that of two-dimensional bodies. Copyright © 2005 John Wiley & Sons, Ltd.