On the relation between Stokes drift and the Gerstner wave

A.A. Abrashkin^a, E.N. Pelinovsky^b
^aNational Research University Higher School of Economics, Nizhny Novgorod Branch, B. Pecherskaya str. 25/12, Nizhny Novgorod, 603155, Russian Federation
^bFederal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

This paper discusses the properties of two-dimensional, nonlinear, potential and vortex waves on the surface of an ideal liquid of infinite depth. It is shown that to quadratic order in the amplitude, the vorticity of the Gerstner wave is equal in magnitude and different in sign to that of the Stokes drift current in a surface layer. This allows a classic Stokes wave obtained in the framework of potential theory to be interpreted as a superposition of the Gerstner wave and Stokes drift. It is proposed that the nonlinearity coefficient in the nonlinear Shrödinger equation can be physically interpreted as the Doppler frequency shift over the vertically averaged Stokes drift current.

Keywords: waves on the water, vorticity, Stokes drift, Gerstner wave, nonlinear Shrödinger equation
PACS: 47.35.Bb
DOI: 10.3367/UFNe.2017.03.038089
URL: https://ufn.ru/en/articles/2018/3/f/
Web of Science

000435395400006
Scopus

2-s2.0-85048380519
ADS NASA

2018PhyU...61..307A
Citation: Abrashkin A A, Pelinovsky E N "On the relation between Stokes drift and the Gerstner wave" Phys. Usp. 61 307–312 (2018)

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Received: 20th, February 2017, accepted: 9th, March 2017

Оригинал: Абрашкин А А, Пелиновский Е Н «О связи дрейфа Стокса и волны Герстнера» УФН 188 329–334 (2018); DOI: 10.3367/UFNr.2017.03.038089