Exact free surfaces in constant vorticity flows

Vera Hur, Miles Wheeler

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Abstract

We present an exact solution for periodic travelling waves in two-dimensional, infinitely deep and constant vorticity flows, in the absence of the effects of gravity or surface tension. The shape of the free surface is the same as for Crapper's celebrated capillary waves in an irrotational flow, but the flow beneath the wave, which is also explicit, is completely different. This confirms a conjecture made by Dyachenko & Hur (J. Fluid Mech., vol. 878, 2019b, pp. 502-521; Stud. Appl. Maths, vol. 142 (2), 2019c, pp. 162-189) and Hur & Vanden-Broeck (Eur. J. Mech. (B/Fluids), 2020, to appear), based on numerical and asymptotic evidence.

Original languageEnglish
Article numberR1
Number of pages10
JournalJournal of Fluid Mechanics
Volume896
Early online date26 May 2020
DOIs
Publication statusE-pub ahead of print - 26 May 2020

Keywords

  • surface gravity waves

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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