Torres, T., Coutant, A., Dolan, S. orcid.org/0000-0002-4672-6523 et al. (1 more author) (2018) Waves on a vortex: rays, rings and resonances. Journal of Fluid Mechanics, 857. pp. 291-311. ISSN 0022-1120
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Cambridge University Press. This is an author produced version of a paper subsequently published in Journal of Fluid Mechanics. Article available under the terms of the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Surface gravity waves; vortex flows; waves/free-surface flows |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 22 Oct 2018 11:37 |
Last Modified: | 22 May 2020 09:22 |
Published Version: | https://doi.org/10.1017/jfm.2018.752 |
Status: | Published |
Publisher: | Cambridge University Press |
Refereed: | Yes |
Identification Number: | 10.1017/jfm.2018.752 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:137508 |