Waves on a vortex: rays, rings and resonances

TL;DR

This paper investigates surface water wave scattering by vortices, revealing unstable orbits analogous to black hole light rings, and predicts observable resonances with potential experimental validation.

Contribution

It introduces a ray-tracing approach to identify vortex orbits analogous to black hole light rings and derives explicit formulas for their properties.

Findings

Existence of unstable co-rotating and counter-rotating orbits around vortices.

Derived an explicit formula for the critical orbit radius in deep water.

Predicted a discrete set of damped resonances that can be observed experimentally.

Abstract

We study the scattering of surface water waves with irrotational draining vortices. At small depth, this system is a mathematical analogue of a rotating black hole and can be used to mimic some of its peculiar phenomenon. Using ray-tracing methods, we exhibit the existence of unstable orbits around vortices at arbitrary depth. These orbits are the analogue of the light rings of a black hole. We show that these orbits come in pairs, one co-rotating and one counter-rotating, at a critical radius that varies with the frequency. We derived an explicit formula for this radius in the deep water regime. Our method is validated by comparison with recent experimental data from a wavetank experiment. We finally argue that these rings will generate a discrete set of damped resonances that we characterize and that could possibly be observed in future experiments.