Analytical solution of oscillating inviscid flow over oblate spheroids with spheres and flat disks as special cases

The hydrodynamic forces acting on an oblate spheroid placed in an oscillating free stream are obtained for the special case of inviscid flow. The flow is assumed incompressible and axisymmetric and the free stream oscillations are harmonic. The flow direction is always along the spheroid's axis of symmetry. Analytical expressions are obtained for the potential and stream functions as well as the surface pressure distribution and the hydrodynamic force coefficient. The analysis is based on the solution of the unsteady equations of motion and continuity in oblate spheroidal coordinate system. The parameters involved are the major to minor axes ratio and the Strouhal number. The solutions for the two limiting cases of oscillating flows over disks and spheres can be easily obtained from the presented analytical solution.