Geodesic
Nonlinear wave on the surface layer of a viscous liquid
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 322-329 
K. Yu. Basinsky. Nonlinear wave on the surface layer of a viscous liquid. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 322-329. http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The nonlinear problem of the propagation of waves on the free surface of the layer of viscous incompressible fluid of infinite depth in the plane case. Using small parameter method, this nonlinear problem is decomposed into problems in the first two approximations that consistently allowed. Nonlinear expressions for the components of the velocity vector, the dynamic pressure and the shape of the free surface. The motion of particles of the viscous fluid caused by the spread of the wave of the free surface. It is found that the viscosity has a significant effect on the shape of the trajectories of liquid particles which is manifested as a decrease in the amplitude of oscillation over time, and in contrast to the paths near the free surface and penetration. The nonlinear effect of Stokes, which is the presence of near-surface currents.

[1] Sretenskiy L. N., Theory of wave motions of fluid, Nauka, M., 1977, 816 pp. (in Russian)

[2] Aleshkov Yu. Z., The theory of waves on the surface of a heavy liquid, Leningrad Univ. Press, Leningrad, 1981, 196 pp. (in Russian)

[3] Lamb G., Hydrodynamics, Gostekhizdat, L., 1947, 928 pp. (in Russian)

[4] Landau L. D., Lifshits E. M., Hydrodynamics, Nauka, M., 1986, 735 pp. (in Russian) | MR

[5] Barinov V. A., “Wave propagation on the free surface of a viscous fluid”, Vestn. S.-Peterb. un-ta, 2010, no. 2, 18–31 (in Russian) | MR

[6] Barinov V. A., Basinsky K. Yu., “The solution of the problem of nonlinear waves on the surface of the low-viscosity fluid”, Vestn. S.-Peterb. un-ta, 2011, no. 2, 9–16 (in Russian)