Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution

TL;DR

This paper investigates the behavior of quantized superfluid vortices on axisymmetric surfaces like ellipsoids, using conformal mappings to analyze vortex dynamics and energy, with a focus on symmetric and asymmetric vortex dipoles.

Contribution

It introduces a conformal transformation approach to study vortex dynamics on curved surfaces, specifically ellipsoids, extending superfluid vortex theory beyond flat geometries.

Findings

Analysis of vortex dipole configurations on ellipsoids.

Identification of symmetric and asymmetric vortex behaviors.

Application of conformal mapping to compute vortex energy.

Abstract

We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal transformation from the surface to the complex plane allows us to use familiar formalism to describe the motion of the quantized vortices and to find the total energy. The simplest case is a vortex dipole with unit vortex charges on an axisymmetric ellipsoid. We study two special symmetric vortex-dipole configurations along with a general asymmetric one.