SINGULARITIES OF THE EULER EQUATION AND HYDRODYNAMIC STABILITY

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived . Under some assumptions, it is shown how this motion is dictated by t he smooth part of the complex velocity at a singular point in the unph ysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equati on. A sufficient condition for instability is conjectured. Several exa mples are presented to demonstrate the efficacy of this sufficient con dition which include the class of elliptical flows and the Kelvin-Stua rt cat's eye.