We investigate, experimentally and numerically, the flow around a
torsionally oscillating sphere. We consider oscillation frequencies
in the range $15\le r\,\sqrt{\omega/2\nu}\le60$, and amplitudes in
the range $0<\Phi_0<3.5$. The flow consists of a radial jet of
periodically fluctuating speed emanating from the equator of the
oscillating 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 $r$ from the
sphere. A 2D 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 gradually emerge, and on
the variation of that range with frequency. Finally, the turbulent
breakdown of the vortices at very high amplitudes is studied
experimentally, and a connection with previous results is suggested.
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