Chiral edge modes in Helmholtz-Onsager vortex systems

Abstract

Vortices play a fundamental role in the physics of two-dimensional (2D) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, point vortices in a 2D fluid continue to pose interesting theoretical problems, owing to their unusual statistical mechanics. Here we show that the strongly interacting Helmholtz-Onsager vortex systems can form statistical edge modes at low energies, extending a previously identified analogy between vortex matter and quantum Hall systems. Through dynamical simulations, Monte-Carlo sampling, and mean-field theory, we demonstrate that these edge modes are associated with the formation of dipoles of real and image vortices at boundaries. The edge modes are robust, persisting in nonconvex domains, and are in quantitative agreement with the mean-field predictions.