Viscous flow near a cusped corner

Abstract

The slow motion of fluid exterior to a cylinder lying on a wall is considered for a variety of boundary conditions. In particular, the solution is obtained for the case when the motion far from the cylinder is one of uniform shear. Calculations are made for the force and the moment exerted by the fluid on the cylinder. The asymptotic form of the flow both far from the cylinder and near the cusped corners is presented. The flow sufficiently near a cusp consists of a sequence of eddies of rapidly diminishing strength, and the solution of another boundary-value problem supports the view that the nature of this eddy system is independent of conditions far from the cusp. The nature of inviscid flow with uniform vorticity in cusped corners is also considered.