The nonlinear evolution of rotating configurations of uniform vorticity

Abstract

The nonlinear evolution of perturbed equilibrium configurations of constant-vorticity vortices is calculated. To illustrate a variety of nonlinear behaviour, we consider the following relatively simple configurations: the corotating configurations of N vortices whose linear stability has been treated in a previous study; the elliptical vortex; and the annular vortex. Our calculations test for nonlinear stability as well as categorize the possible forms of stability and instability. The energy ideas announced in the previous study are found to greatly constrain vortex evolution. In particular, we show that two vortices and an elliptical vortex may evolve into each other, and that an annular vortex may break cleanly into five co-rotating vortices.