The flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid

Abstract

A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophic flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.