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Waves on a vortex: rays, rings and resonances

Torres, Theo; Coutant, Antonin; Dolan, Sam; Weinfurtner, Silke


Theo Torres

Antonin Coutant

Sam Dolan


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 phenomena. 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 an orbital 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.


Torres, T., Coutant, A., Dolan, S., & Weinfurtner, S. (2018). Waves on a vortex: rays, rings and resonances. Journal of Fluid Mechanics, 857, 291-311.

Journal Article Type Article
Acceptance Date Oct 15, 2018
Online Publication Date Oct 22, 2018
Publication Date Dec 25, 2018
Deposit Date Jan 12, 2019
Publicly Available Date Apr 23, 2019
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 857
Pages 291-311
Keywords Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
Public URL
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