A CIRCLE THEOREM FOR PLANE STOKES FLOWS
Arun Avudainayagam, B. Jothiram · The Quarterly Journal of Mechanics and Applied Mathematics · 1988
The problem of plane Stokes flow of a viscous incompressible fluid in the unbounded region exterior to a circular cylinder is considered. In a recent communication (1), assuming the conditions of zero velocity at infinity and a prescribed velocity vector V = F(θ) on the contour of the cylinder, it was shown that a necessary condition for the existence of a Stokes solution is that the boundary function F(θ) must satisfy a consistency condition. In this paper, we consider the problem in terms of the biharmonic stream function. Necessary conditions for the existence of a solution of the two-dimensional biharmonic equation in the region exterior to a circle are established. A circle theorem is also derived for plane Stokes flows and a few representative examples are given.