Geodesic
The asymptotic solution of a~nonlinear problem of wave propagation on a~surface of viscous fluid
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 397-404

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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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     author = {K. Yu. Basinsky},
     title = {The asymptotic solution of a~nonlinear problem of wave propagation on a~surface of viscous fluid},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {397--404},
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     volume = {25},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a9/}
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K. Yu. Basinsky. The asymptotic solution of a~nonlinear problem of wave propagation on a~surface of viscous fluid. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 397-404. http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a9/