Compressible flow past a contour and stationary vortices

Abstract

The Rayleigh-Janzen expansion method is extended to plane and steady flows which contain one or more point vortices interacting with a smooth or sharp-edged obstacle. A uniformly valid approximate solution of the compressible-flow equations is deduced by applying a perturbation method and by using matched asymptotic expansions to solve the resulting singular perturbation problem. The method yields compressibility corrections for the vortex positions and for the velocities. Results are presented for the flow past a circle and a pair of symmetric vortices (Föppl's flow). They show that the compressibility effects are substantial and are consistent with experimental data.