The flow induced at a wall by a vortex pair

The motion of a counter-rotating pair of two-dimensional vortices above a plane wall is considered. The vortices are assumed to be initially placed in an otherwise stagnant and incompressible fluid above the wall. Depending on the assumed sense of rotation, the vortices either recede from the wall or move toward it, at an angle of attack; both situations are considered. Numerical solutions are obtained for the unsteady viscous boundary-layer flow that develops on the wall due to the vortex motion. In all cases, separation occurs in the boundary layer in the form of the appearance of secondary eddies; in addition, explosive boundary-layer growth is invariably observed near these eddies. The results suggest that the boundary-layer flow will ultimately erupt into the inviscid region in a strong viscous-inviscid interaction with the outer flow. The relation of these results to recent experimental work is discussed.