Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution

We present a study of superfluid vortex dynamics on general axisymmetric compact surfaces with no holes. Specifically, we develop a general method to transform conformally from the axisymmetric surface to a plane, where we use familiar methods based on the hydrodynamic stream function. Our approach shows that vortices constitute a Hamiltonian dynamical system, with their angular positions on the surface as canonical variables. The dynamical motion conserves both the total energy and the angular momentum, and it features a marked anticorrelation between the vortex speed and the local curvature of the surface.

Automated summary

This study presents an investigation into the dynamics of superfluid vortices on general axisymmetric compact surfaces without any holes. By transforming the axisymmetric surface conformally to a plane, a general method is developed using hydrodynamic stream function. The research reveals that vortices constitute a Hamiltonian dynamical system with the angular positions on the surface serving as canonical variables. The dynamical motion conserves both the total energy and angular momentum, and it shows a significant anticorrelation between vortex speed and local surface curvature.