Exact free surfaces in constant vorticity flows. (10th August 2020)

• Record Type: Journal Article
• Authors: Hur, Vera Mikyoung; Wheeler, Miles H.
• Is Part Of: Journal of fluid mechanics. Volume 896(2020)
• Publication Date: 2020-08-10
• Subjects: surface gravity waves; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.390
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : 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, 2019 b, pp. 502–521; Stud. Appl. Maths, vol. 142 (2), 2019 c, pp. 162–189) and Hur & Vanden-Broeck ( Eur. J. Mech. (B/ Fluids ), 2020, to appear), based on numerical and asymptotic evidence.