Some steady vortex flows past a circular cylinder

Steady vortex flows past a circular cylinder are obtained numerically as so lutions of the partial differential equation Delta Psi = f(Psi), f(Psi) = o mega(1 - H(Psi - alpha)), where H is the Heaviside function. Only symmetric solutions are considered so the flow may be thought of as that past a semi circular bump in a half-plane. The flow is transplanted by the complex loga rithm to a semi-infinite strip. This strip is truncated at a finite height, a numerical boundary condition is used on the top, and the difference equa tions resulting from the Ave-point discretization for the Laplacian on a un iform grid are solved using Fourier methods and an iteration for the nonlin ear equation. If the area of the vortex region is prescribed the magnitude of the vorticity w is adjusted in an inner iteration to satisfy this area c onstraint. Three types of solutions are discussed: vortices attached to the cylinder, vortex patches standing off from the cylinder and strips of vorticity exten ding to infinity. Three families of each type of solution have been found. Equilibrium positions for point vortices, including the Foppl pair, are rel ated to these families by continuation.