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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 3, Pages 397–404 (Mi vuu494)

MECHANICS

The asymptotic solution of a nonlinear problem of wave propagation on a surface of viscous fluid

K. Yu. Basinsky

Department of Mathematical Modelling, Tyumen State University, ul. Semakova, 10, Tyumen, 625003, Russia

Abstract: The paper deals with the nonlinear problem of wave propagation on a free surface of an infinitely deep layer of viscous incompressible fluid on a plane. Using the method of a small parameter, this nonlinear problem is decomposed into problems at the first two approximations which are solved one by one. Nonlinear expressions for the components of a velocity vector, the dynamic pressure and the shape of a free surface are obtained. The motion of viscous fluid particles caused by wave propagation on a free surface is investigated. It is found that the viscosity of a liquid has significant effect on the shape of the trajectories of liquid particles, which is manifested as a decrease in the amplitude of oscillations over time, and in the trajectories dissimilarity near the free surface, and at the deepening. The nonlinear Stokes effect that indicates the presence of near-surface currents is analyzed.

Keywords: viscosity, wave motion, the particle trajectories.

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UDC: 532.591
MSC: 76D33

Citation: K. Yu. Basinsky, “The asymptotic solution of a nonlinear problem of wave propagation on a surface of viscous fluid”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:3 (2015), 397–404

Citation in format AMSBIB
\Bibitem{Bas15} \by K.~Yu.~Basinsky \paper The asymptotic solution of a~nonlinear problem of wave propagation on a~surface of viscous fluid \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2015 \vol 25 \issue 3 \pages 397--404 \mathnet{http://mi.mathnet.ru/vuu494} \elib{http://elibrary.ru/item.asp?id=24237246}