Unsteady separation for Stokes flows in two dimensions

Abstract

Some simple solutions are presented to the unsteady Stokes flow equations which describe the development of the slow viscous flow due to a line rotlet. Four different geometries are considered, with the rotlet (a) in front of a plane wall, (b) inside a circular cylinder, (c) outside a circular cylinder, (d) between two parallel walls; also, the development is considered (i) after the impulsive introduction of a potential vortex, and (ii) after the impulsive introduction of a line source of angular momentum. Separation occurs in all these situations, and one is able to trace the movement of the separation points, and the formation of eddies, for different times. A number of distinctive physical phenomena are detected.