Eigenfrequencies of vortex-pair equilibria near an elliptic cylinder or a flat plate in uniform flow

Abstract

The eigenfrequencies of the potential-flow equilibria of a symmetric vortex pair behind an elliptic cylinder in uniform flow are calculated through the use of conformal mapping. These frequencies are shown to have values in agreement with measured Strouhal numbers reported in various papers. The special cases of the potential-flow equilibrium of a symmetric vortex pair behind a circular cylinder and the equilibrium behind a flat plate perpendicular to the uniform flow, are related to the measured Strouhal numbers of about 0.21 and 0.15, respectively. It is suggested that in the range of subcritical Reynolds numbers, 3x10(2) to 5x10(5) for the circular cylinder, a part of the drag is the result of the presence of a mean recirculation region in the near wake, which sheds vortices in the far wake and which is fed by vorticity from the cylinder wall.