  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.
