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Exact Solutions for Layered Three-Dimensional Nonstationary Isobaric Flows of a Viscous Incompressible Fluid

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Abstract

This paper describes an overdetermined system of equations that describe three-dimensional layered unsteady flows of a. viscous incompressible fluid at a. constant pressure. Studying the compatibility of this system makes it possible to reduce it to coupled quasilinear parabolic equations for velocity components. The reduced equations allow constructing several classes of exact solutions. In particular, polynomial and spatially localized self-similar solutions of the equations of motion are obtained. The transition to the ideal fluid limit is investigated.

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Authors and Affiliations

  1. Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620016, Russia

    N. M. Zubarev

  2. Lebedev Physical Institute, Russian Academy of Science, Moscow, 119991, Russia

    N. M. Zubarev

  3. Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620016, Russia

    E. Yu. Prosviryakov

Authors
  1. N. M. Zubarev
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  2. E. Yu. Prosviryakov
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Correspondence to N. M. Zubarev.

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Original Russian Text © N.M. Zubarev, E.Yu. Prosviryakov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 6, pp. 65–71, November-December, 2019.

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Zubarev, N.M., Prosviryakov, E.Y. Exact Solutions for Layered Three-Dimensional Nonstationary Isobaric Flows of a Viscous Incompressible Fluid. J Appl Mech Tech Phy 60, 1031–1037 (2019). https://doi.org/10.1134/S0021894419060075

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  • DOI: https://doi.org/10.1134/S0021894419060075

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