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

Vera Mikyoung Hur, Jean-Marc Vanden-Broeck

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)190-194
Number of pages5
JournalEuropean Journal of Mechanics, B/Fluids
Volume83
DOIs
StatePublished - Sep 1 2020

Keywords

  • Capillarity (surface tension)
  • Constant vorticity
  • Exact solutions
  • Free surface flows

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)

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