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Uspekhi Fizicheskikh Nauk, 2018, Volume 188, Number 3, Pages 329–334
DOI: https://doi.org/10.3367/UFNr.2017.03.038089 (Mi ufn5944) 		 
This article is cited in 6 scientific papers (total in 6 papers)

METHODOLOGICAL NOTES

On the relation between Stokes drift and the Gerstner wave

A. A. Abrashkina, E. N. Pelinovskyb

a National Research University Higher School of Economics, Nizhny Novgorod Branch
b Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod
Full-text PDF (590 kB) Citations (6)
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DOI: https://doi.org/10.3367/UFNr.2017.03.038089
Abstract: We discuss the properties of two-dimensional, nonlinear, potential, and vortex waves on the surface of an ideal liquid of infinite depth. It is shown that in the quadratic order in the amplitude, the vorticity of the Gerstner wave is equal in magnitude to and different in sign from 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 along the vertically averaged Stokes drift current.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 5.5176.2017/8.9
Ministry of Education and Science of the Russian Federation НШ-2685.2018.5
The work was carried out in the framework of a state assignment in the area of scientific research (Assignment No. 5.5176.2017/8.9) and with financial support through a grant from the President of RF for state support of scientific schools, RF-NSh-2685.2018.5.
Received: February 20, 2017
Accepted: March 9, 2017
English version:
Physics–Uspekhi, 2018, Volume 61, Issue 3, Pages 307–312
DOI: https://doi.org/10.3367/UFNe.2017.03.038089
Bibliographic databases:
Document Type: Article
PACS: 47.35.Bb
Language: Russian
Citation: A. A. Abrashkin, E. N. Pelinovsky, “On the relation between Stokes drift and the Gerstner wave”, UFN, 188:3 (2018), 329–334; Phys. Usp., 61:3 (2018), 307–312
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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