TY - JOUR
T1 - Exact free surfaces in constant vorticity flows
AU - Hur, Vera Mikyoung
AU - Wheeler, Miles H.
N1 - Publisher Copyright:
© 2020 The Author(s),. Published by Cambridge University Press.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/8/10
Y1 - 2020/8/10
N2 - 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.
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.
KW - surface gravity waves
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U2 - 10.1017/jfm.2020.390
DO - 10.1017/jfm.2020.390
M3 - Article
SN - 0022-1120
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - R1
ER -