a1 Department of Mathematics, Massachusetts Institute of Technology 2-384, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
a2 Department of Mechanical Engineering, Massachusetts Institute of Technology 3-335, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
This paper demonstrates that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected planar domain bounded by impenetrable walls. A general numerical scheme is presented based on this formulation. The algorithm makes use of conformal mappings and follows the evolution of a conformal pre-image of a given vortex patch in a canonical multiply connected circular pre-image region. The evolution of vortex patches can be computed given just the conformal map from this pre-image region to the physical fluid region. The efficacy of the scheme is demonstrated by illustrative examples.
(Received September 26 2006)
(Revised August 18 2007)