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 boundarylayer 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.