Waves on a vortex: rays, rings and resonances

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

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 (CUP)
• 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