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Section
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Mechanics
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Title
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The trajectories of the particles of a viscous fluid under wave motion
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Author(-s)
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Basinskii K.Yu.a
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Affiliations
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Tyumen State Universitya
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Abstract
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The motion of the particles of a viscous incompressible fluid caused by the proliferation of free surface waves of small amplitude is considered. The equations of motion of fluid particles in the presence of a traveling or a standing wave on the surface of an infinitely deep layer are obtained.
At the propagation of a traveling wave the trajectories are spirals the centers of which correspond to a state of rest. The effect of viscosity is manifested as a decrease in the amplitude of oscillations over time, as well as by the fact that the trajectories of particles near the free surface and at burial are of different form. In the case of a standing wave the motion of each particle goes at intervals the length of which decreases with time. The direction of motion changes from the vertical at the antinodes to the horizontal at the nodes.
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Keywords
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viscosity, wave motion, particle trajectories
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UDC
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532.591
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MSC
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76D33
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DOI
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10.20537/vm150209
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Received
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4 June 2015
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Language
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Russian
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Citation
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Basinskii K.Yu. The trajectories of the particles of a viscous fluid under wave motion, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 2, pp. 248-253.
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References
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- Sretenskii L.N. Teoriya volnovykh dvizheniy zhidkosti (Theory of wave motions of fluid), Moscow: Nauka, 1977, 816 p.
- Aleshkov Yu.Z. Teoriya voln na poverkhnosti tyazheloi zhidkosti (The theory of waves on the surface of a heavy liquid), Leningrad: Leningrad State University, 1981, 196 p.
- Barinov V.A., Taktarov N.G. Matematicheskoe modelirovanie magnitogidrodinamicheskikh poverkhnostnykh voln (Mathematical modeling of MHD surface waves), Saransk: Mordovia State University, 1991, 96 p.
- Levich V.G. Fiziko-khimicheskaya gidrodinamika (Physico-chemical hydrodynamics), Moscow: Fizmatgiz, 1959, 700 p.
- Barinov V.A. Distribution of waves on free surface of viscous liquid, Vestn. St-Peterbg. Univ., Ser. 10, Prikl. Mat. Inf. Prots. Upr., 2010, vol. 10, no. 2, pp. 18-31 (in Russian).
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Full text
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