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Unsteady layered vortical fluid flows

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Abstract

An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette flow. Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered. These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed. It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary.

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Authors and Affiliations

  1. Institute of Engineering Science, Ural Branch of the Russian Academy of Sciences, ul. Komsomolskaya 34, Ekaterinburg, 620049, Russia

    S. N. Aristov & E. Yu. Prosviryakov

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  1. S. N. Aristov
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  2. E. Yu. Prosviryakov
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Correspondence to E. Yu. Prosviryakov.

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Original Russian Text © S.N. Aristov, E.Yu. Prosviryakov, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2016, Vol. 51, No. 2, pp. 25–31.

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Aristov, S.N., Prosviryakov, E.Y. Unsteady layered vortical fluid flows. Fluid Dyn 51, 148–154 (2016). https://doi.org/10.1134/S0015462816020034

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