STEADY STREAMING DUE TO SMALL-AMPLITUDE SUPERPOSED OSCILLATIONS OF A SPHERE IN A VISCOUS-FLUID

The flow induced by the small-amplitude, isoharmonic, coaxial transverse and torsional oscillations of a sphere in a viscous fluid is considered. The method of matched asymptotic expansions is used to treat principally the second-order streaming flow generated in the low- and high-frequency limits. It is found that the ratio of the amplitudes and the difference in the phase, ot the oscillations in the two directions, are important in determining the nature of this time-independent motion. The combined oscillations give rise to a steady hemispherically-antisymmetric azimuthal swirl component in the flow in addition to the hemispherically-symmetric streaming motion induced in the meridional planes. For large-streaming Reynolds numbers the flow assumes a well-known double-boundary-layer structure which is accompanied by an eruption of the fluid into jets with swirl.