CONSTANT VORTICITY RIABOUCHINSKY FLOWS FROM A VARIATIONAL PRINCIPLE

Flows with constant vorticity regions bounded by vortex sheets are obtained by minimizing a functional which is the difference of energy in the external (irrotational) flow and the internal flow. In the zero vorticity case this reduces to the functional used by Garabedian, Lewy, and Schiffer for Riabouchinsky's problem. The discretization is done using Schwarz-Christoffel transformations for approximating polygons and FFT's to compute required Dirichlet integrals.