ROTATING N-GON KN-GON VORTEX CONFIGURATIONS

We demonstrate the existence of stationary point-vortex configurations consisting of k vortex n-gons and a vortex kn-gon. These configuratio ns exist only for specific values of the vortex strengths; the relativ e vortex strengths of such a configuration can be uniquely expressed a s functions of the radii of the polygons. The kn-gon must be oriented so as to be fixed by any reflection fixing one of the n-gons; for suff iciently small k, we show that the n-gons must be oriented in such a w ay that the entire configuration shares the symmetries of any of the n -gons. Necessary conditions for the formal stability of general statio nary point-vortex configurations set conditions on the vortex strength s. We apply these conditions to the n-gon/kn-gon configurations and ca rry out a complete linear and formal stability analysis in the case k = n = 2, showing that linearly and nonlinearly orbitally stable config urations exist.