PLANAR RELATIVE EQUILIBRIUM VORTICES WITH FREE BOUNDARIES

A variational characterization is employed to find isolated vortices-s teady solutions of the two-dimensional Euler equations-as relative equ ilibrium solutions. The steady states are parametrized by the values o f invariant integrals of the dynamical system corresponding to the phy sical quantities of enstrophy, positive and negative circulation and l inear and angular momentum. The variational principles can be treated analytically in special configurations but are solved numerically in o ther cases, where the optimization scheme by Eydeland solves for the f ree boundaries. We find continuous distributions of vorticity on suppo rts that are not necessarily simply connected. For special choices of the parameter values isolated mono-, di-, tri- and quadrupolar vortice s are found.