THE FORCE ON A SPHERE IN A UNIFORM-FLOW WITH SMALL-AMPLITUDE OSCILLATIONS AT FINITE REYNOLDS-NUMBER

The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number, Re. Good agreement is hown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re almost-equal-to 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.