Fluctuating flow induced by a rotating disc

Abstract

Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular velocity Ω(a + b cos ωT) in contact with an incompressible viscous fluid of semi-infinite extent is analysed when the ampli­tude parameter α ( = b/a) varies from zero to infinity. Composite solutions valid over the whole of the flow régime and specific expressions for the shearing stress components at the disc and for the axial flow in the far region are obtained for low and high frequencies of periodic fluctuations. An attempt is made to calculate the frequency of overlap of the two solutions. Using the method of matched asymptotic expansions, we find that the thickness of the region of mean flow increases with α. New esti­mates of the thickness of the outer region are obtained for the fluid motion induced by torsional oscillations of a plane lamina.