The N-vortex problem on a symmetric ellipsoid: A perturbation approach

Abstract

We consider the N-vortex problem on an ellipsoid of revolution. Applying standard techniques of classical perturbation theory, we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations, the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid’s generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three vortex system on the symmetric ellipsoid is nonintegrable.