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

The flow induced by the small-amplitude torsional oscillations of a sphere in a viscous fluid is considered with particular emphasis on the second-order streaming motion. The method of matched asymptotic expansions is used in a manner similar to Riley (Q. Jl Mech. appl. Math. 19 (1966) 461-472) to treat both the low- and high-frequency limits. For the case of small streaming Reynolds numbers in the high-frequency limit, the structure of the inner and outer expansions of the time-independent terms is established in some detail. For the case of large streaming Reynolds numbers, the outer boundary-layer nature of the streaming motion is numerically determined. The similarity solution for a radial free jet is used to describe the equatorial jet resulting from the collision of these boundary layers.