Exact free surfaces in constant vorticity flows

Vera Hur; Miles Wheeler

doi:10.1017/jfm.2020.390

Exact free surfaces in constant vorticity flows

Vera Hur, Miles Wheeler

Department of Mathematical Sciences

University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

13 Citations (SciVal)

165 Downloads (Pure)

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 language	English
Article number	R1
Number of pages	10
Journal	Journal of Fluid Mechanics
Volume	896
Early online date	26 May 2020
DOIs	https://doi.org/10.1017/jfm.2020.390
Publication status	Published - 1 Aug 2020

Keywords

surface gravity waves

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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AB - 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.

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Exact free surfaces in constant vorticity flows

Abstract

Keywords

ASJC Scopus subject areas

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