Theo Torres
Waves on a vortex: rays, rings and resonances
Torres, Theo; Coutant, Antonin; Dolan, Sam; Weinfurtner, Silke
Authors
Antonin Coutant
Sam Dolan
Professor SILKE WEINFURTNER SILKE.WEINFURTNER@NOTTINGHAM.AC.UK
PROFESSOR OF MATHEMATICAL SCIENCES
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 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.
Citation
Torres, T., Coutant, A., Dolan, S., & Weinfurtner, S. (2018). Waves on a vortex: rays, rings and resonances. Journal of Fluid Mechanics, 857, 291-311. https://doi.org/10.1017/jfm.2018.752
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 |
Peer Reviewed | Peer Reviewed |
Volume | 857 |
Pages | 291-311 |
DOI | https://doi.org/10.1017/jfm.2018.752 |
Keywords | Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics |
Public URL | https://nottingham-repository.worktribe.com/output/1466553 |
Publisher URL | https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/waves-on-a-vortex-rays-rings-and-resonances/B3C0CA073270174B92E61C45128F0D87 |
Contract Date | Jan 12, 2019 |
Files
Analogue Geodesic Jfm V3
(1.5 Mb)
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