Equilibrium shapes of a pair of equal uniform vortices

Abstract

The shapes and properties of two equal corotating uniform vortices, rotating steadily about each other, are calculated. An integrodifferential equation for the bounding contour is solved numerically, using Newton’s method. The results compare well with those obtained from a simple model. It is shown that steady solutions do not exist if the vortices are too close. The stability to two-dimensional disturbances is discussed qualitatively and the critical separation at which the system becomes unstable is calculated. Some comments are made on the stability of a vortex pair of equal counter rotating uniform vortices.