The flow around a torsionally oscillating sphere

We investigate, experimentally and numerically, the flow around a torsionally oscillating sphere. The oscillation frequency is sufficiently high that the thickness of the Stokes boundary layer is small compared with the radius of the sphere. In addition to this boundary layer the flow then consists of a radial jet of periodically fluctuating speed emanating from the equator of the sphere. As the oscillation amplitude is increased, these fluctuations gradually become more pronounced, until the faster portions of the jet overtake the slower ones, causing them to curl back on themselves to form vortex pairs. The experimental results show that even after the appearance of the vortices the flow remains predominantly axisymmetric, and also equatorially symmetric, for a distance considerably greater than one sphere radius away. A two-dimensional numerical code is therefore used to elucidate the precise details of the flow, with excellent agreement on the range of amplitudes over which the vortices and other structures gradually emerge, and on the variation of that range with frequency. The turbulent breakdown of the vortices at higher amplitudes is also studied experimentally, and a connection with previous results is suggested.