Thursday 16 Jan 2014: Vortex dynamics on surfaces of revolution (Taylor and Francis sponsored)
Stefanella Boatto -
Harrison 101 15:00-16:00
Many key features of the motion of satellites, planets, stars, even galaxies can be captured by point mass dynamics. Likewise, many key features of fluid motion such as atmospheric storms, ocean eddies, super fluid vortices, and early stages of mass aggregation in gravitational systems can be captured by point vortex dynamics. Yet, serious mathematical challenges remain. Systems consisting of more than a few points are non-integrable, and complexity increases dramatically with the number of particles. Furthermore, the underlying geometry has a profound influence on the particle motion, as has only just begun to be investigated. Indeed one of today's challenges is a formulation of the N-vortex dynamics on Riemann surfaces. There are formulations over surfaces with constant Gaussian curvature, and lately, for surfaces with not constant Gaussian curvature, conformal to the sphere. We present some results about vortex dynamics on surfaces of revolution (among others the sphere and the ellipsoid of rotation). We obtain a vortex equivalence principle: variations of the Gaussian curvature generate dynamics. A single vortex on an ellipsoid would move.
In collaboration with Jair Koiller (FGV, Rio de Janeiro) and David Dritschel (University of St. Andrews)