Instability of a Vortex Sheet Leaving a Semi‐Infinite Plate

Abstract

The growth of undulations along an infinite vortex sheet is a classical problem of stability theory. Here we modify that problem by including the effects of a boundary: the vortex sheet is assumed to leave a rigid semi‐infinite plate and to undergo spatially growing undulations downstream. The usual solution for a doubly infinite sheet is corrected by the Wiener‐Hopf technique to account for the presence of the plate. The correction depends sensitively on whether a Kutta condition is enforced at the trailing edge. Two Kutta conditions, called rectified and full, are suggested to apply depending on conditions in the unperturbed flow. In either case, the correction due to the plate becomes negligible half a wavelength downstream from the trailing edge.