@article { , title = {Waves on a vortex: rays, rings and resonances}, 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.}, doi = {10.1017/jfm.2018.752}, eissn = {1469-7645}, issn = {0022-1120}, journal = {Journal of Fluid Mechanics}, note = {6 mo. embargo. OL 14.01.2019}, pages = {291-311}, publicationstatus = {Published}, publisher = {Cambridge University Press (CUP)}, url = {https://nottingham-repository.worktribe.com/output/1466553}, volume = {857}, keyword = {Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics}, year = {2018}, author = {Torres, Theo and Coutant, Antonin and Dolan, Sam and Weinfurtner, Silke} }