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A new application of Crapper’s exact solution to waves in constant vorticity flows

Hur, VM; Vanden-Broeck, J-M; (2020) A new application of Crapper’s exact solution to waves in constant vorticity flows. European Journal of Mechanics - B/Fluids , 83 pp. 190-194. 10.1016/j.euromechflu.2020.04.015.

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Abstract

In 1957, Crapper found an exact solution for capillary waves in an irrotational flow of infinite depth. Here we provide asymptotic and numerical evidence that a Crapper wave makes the profile of a periodic traveling wave in a constant vorticity flow when the effects of gravity and surface tension are negligible. This is achieved by explicitly constructing successive approximate solutions for small amplitude waves and numerically computing arbitrary amplitude waves.

Type: Article
Title: A new application of Crapper’s exact solution to waves in constant vorticity flows
DOI: 10.1016/j.euromechflu.2020.04.015
Publisher version: https://doi.org/10.1016/j.euromechflu.2020.04.015
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Free surface flows, Exact solutions, Capillarity (surface tension), Constant vorticity
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10106067
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