Exact free surfaces in constant vorticity flows

Vera Hur, Miles Wheeler

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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
Early online date26 May 2020
Publication statusPublished - 1 Aug 2020


  • surface gravity waves

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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