Oscillating viscous flow over a sphere

This paper deals with the problem of oscillating viscous flow over a sphere. The flow is assumed axisymmetric and governed by the Navier-Stokes equations for incompressible fluids. The method of solution is based on the series truncation method where the stream function and vorticity are expressed in terms of a finite series of Legendre and first associated Legendre functions. The effects of the Reynolds and Strouhal numbers on the flow characteristics are studied and compared with available data from previous work and also from potential flow solutions. Results are presented for periodic variation of the drag coefficient, surface vorticity and pressure distributions for Reynolds numbers ranging from 5 to 200. The time variation of the velocity field during one complete oscillation is presented in the form of streamline and equivorticity patterns. The periodic variation of the angle of separation as well as the length of the separation bubble are also presented. Calculations are performed for the time-averaged stream function and vorticity through which the double boundary layer structure is confirmed for the range of Reynolds and Strouhal numbers considered.