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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 2, Pages 112–122 (Mi vuu220)  

This article is cited in 2 scientific papers (total in 2 papers)

MECHANICS

Nonlinear Stokes waves on the surface of low-viscosity fluid

V. A. Barinov, K. Yu. Basinsky

Tyumen State University, Tyumen, Russia

Abstract: The statements of nonlinear boundary-value problem for wave propagation over the free surface of low-viscosity fluid have been presented. Solution is found by the method of time-varying frequency, which is the Stokes' method generalized for the dissipative wave processes. The asymptotic solution up to the third-order approximation upon the wave parameter has been found. It is shown that the frequency and damping rate of the nonlinear wave tend in time to the values corresponding to a linear problem. Nonlinear trajectories of fluid particles and the expression for transfer velocity in a low-viscosity Stokes fluid have been defined.

Keywords: nonlinear surface waves, viscous dissipation, dispersion relations.

Full text: PDF file (203 kB)
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UDC: 517.957+532.591+532.133
MSC: 76D33, 35Q30
Received: 27.01.2011

Citation: V. A. Barinov, K. Yu. Basinsky, “Nonlinear Stokes waves on the surface of low-viscosity fluid”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2, 112–122

Citation in format AMSBIB
\Bibitem{BarBas11}
\by V.~A.~Barinov, K.~Yu.~Basinsky
\paper Nonlinear Stokes waves on the surface of low-viscosity fluid
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 2
\pages 112--122
\mathnet{http://mi.mathnet.ru/vuu220}


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    This publication is cited in the following articles:
    1. Abrashkin A.A., Bodunova Yu.P., “Nonlinear Standing Waves on the Surface of a Viscous Fluid”, Fluid Dyn., 47:6 (2012), 725–734  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. V. A. Barinov, K. Yu. Basinskii, “Nelineinye volny na svobodnoi poverkhnosti dvukhfaznoi sredy”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 3, 130–139  mathnet
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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