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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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  • https://www.mathnet.ru/eng/ufn5944
  • https://www.mathnet.ru/eng/ufn/v188/i3/p329
    • This publication is cited in the following 6 articles:
    1. Yan Li, Amin Chabchoub, “How Currents Trigger Extreme Sea Waves. The Roles of Stokes Drift, Eulerian Return Flow, and a Background Flow in the Open Ocean”, Geophysical Research Letters, 51:6 (2024)  crossref
    2. A. A. Abrashkin, E. N. Pelinovsky, “Cauchy invariants and exact solutions of nonlinear equations of hydrodynamics”, Theoret. and Math. Phys., 215:2 (2023), 599–608  mathnet  crossref  crossref  mathscinet  adsnasa
    3. A. A. Abrashkin, E. N. Pelinovsky, “Two ways to generalize Gerstner waves in the theory of waves in deep water”, Radiophys. Quantum El., 66:2-3 (2023), 116  crossref
    4. N. Pizzo, L. Lenain, O. Rømcke, S. Å. Ellingsen, B. K. Smeltzer, “The role of Lagrangian drift in the geometry, kinematics and dynamics of surface waves”, J. Fluid Mech., 954 (2023)  crossref
    5. A. A. Abrashkin, E. N. Pelinovsky, “Gerstner waves and their generalizations in hydrodynamics and geophysics”, Phys. Usp., 65:5 (2022), 453–467  mathnet  crossref  crossref  adsnasa  isi
    6. H. Weber Jan Erik, “A Lagrangian study of internal Gerstner- and Stokes-type gravity waves”, Wave Motion, 88 (2019), 257–264  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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