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Large-scale flows of viscous incompressible vortical fluid

  • Aero- and Gas-Dynamics of Flight Vehicles and Their Engines
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Abstract

An exact solution of the Navier - Stokes equations is given that describes the vorticity of a viscous incompressible liquid or gas, dissipative mediums, stationary shear counter-current of continuous vortical medium in the absence of the Coriolis field.

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References

  1. Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika (Theoretical Physics), Moscow: Fizmatlit, 2006, vol. 6, 736 p.

    Google Scholar 

  2. Aristov, S.N., Knyazev, D.V., and Polyanin, A.D., Exact Solutions of the Navier-Stokes Equations with the Linear Dependence of Velocity Components on Two Space Variables, Theoretical Foundations of Chemical Engineering, 2009, vol. 43, no. 5, pp. 642–662.

    Article  Google Scholar 

  3. Aristov, S.N. and Prosviryakov, E.Yu., Inhomogeneous Couette Flows, Nelineinaya Dinamika, 2013, vol. 9, no. 4, pp. 177–182.

    MATH  Google Scholar 

  4. Drazin, P.G. and Riley, N., The Navier–Stokes Equations: A Classification of Flows and Exact Solutions. Cambridge: Cambridge Univ. Press, 2006, 196 p.

    Book  MATH  Google Scholar 

  5. Pukhnachev, V.V., Symmetries in the Navier–Stokes Equations, Uspekhi Mekhaniki, 2006, vol. 4, no. 1, pp. 3–76.

    Google Scholar 

  6. Couette, M., Études sur le Frottement des Liquides, Annales de Chimie and de Physique, 1890, Sér. 6, vol.21, pp.433–510.

    MATH  Google Scholar 

  7. Pukhnachev, V.V. and Pukhnacheva, T.P., The Couette Problem for Kelvin–Voigt Medium, Vestnik NGU. Ser. Matematika, Mekhanika, Informatika, 2010, vol. 10, no. 3, pp. 94–109.

    MathSciNet  MATH  Google Scholar 

  8. Skul’skii, O.I. and Aristov, S.N., Mekhanika anomal’no vyazkih zhidkostei (Mechanics of Quasiviscous Liquids), Izhevsk: NPTs Regulyarnaya i Khaoticheskaya Dinamika, 2003.

    Google Scholar 

  9. Protsenko, V.I. and Protsenko, I.G., Asymptotic Model for the Evolution of Perturbations in the Plane Couette-Poiseuille Flow, Doklady Mathematics, 2006, vol. 74, no. 3, pp. 896–900.

    Article  MATH  Google Scholar 

  10. Troshkin, O.V., Nonlinear Stability of Couette, Poiseuille, and Kolmogorov Plane Channel Flows, Doklady Mathematics, 2012, vol. 85, no. 2, pp. 181–185.

    MathSciNet  MATH  Google Scholar 

  11. Rudyak, V.Ya., Isakov E.B., and Bord, E.G., Instability of Plane Couette Flow of Two-Phase Liquids, Technical Physics Letters, 1998, vol. 24, no. 3, pp. 199–200.

    Article  Google Scholar 

  12. Shalybkov, D.A., Hydrodynamic and Hydromagnetic Stability of the Couette Flow, Physics–Uspekhi, 2009, vol. 52, no. 9, pp. 915–935.

    Google Scholar 

  13. Georgievskii, D.V., Generalized Joseph Estimates of Stability of Plane Shear Flows with Scalar Nonlinearity, Bulletin of the Russian Academy of Sciences: Physics, 2011, vol. 75, no. 1, pp. 140–143.

    Article  MATH  Google Scholar 

  14. Boronin, S.A., Stability of the Plane Couette Flow of a Disperse Medium with a Finite Volume Fraction of the Particles, Fluid Dynamics, 2011, vol. 46, no. 1, pp. 64–71.

    Article  MathSciNet  MATH  Google Scholar 

  15. Kudinov, V.A. and Kudinov, I.V., Calculation of Exact Analytic Solutions of Hyperbolic Equations of Motion in the Accelerated Couette Flow, Izv. Rossiiskoi Akademii Nauk. Energetika, 2012, no. 1, pp. 119–133.

    Google Scholar 

  16. Babkin, V.A., Plane Turbulent Couette Flow, Journal of Engineering Physics and Thermophysics, 2003, vol. 76, no. 6, pp. 1251–1254.

    Article  Google Scholar 

  17. Abramyan, A.K., Mirantsev, L.V., and Kuchmin, A.Yu., Modeling of Processes at the Couette Simple Fluid Flow in Flat Nanoscopic Channel, Matematicheskoe Modelirovanie, 2012, vol. 24, no. 4, pp. 3–21.

  18. Malyshev, V.A. and Manita, A.D., Stochastic Micromodel of the Couette Flow, Theory Probab. Appl., 2008, vol. 53, no. 4, pp. 716–727.

    Article  MathSciNet  MATH  Google Scholar 

  19. Belyaeva, N.A. and Kuznetsov, K.P., Analysis of a Nonlinear Dynamic Model of the Couette Flow for Structured Liquid in a Flat Gap, Vestnik Samarskogo Gos. Tekh. Univ. Ser. Fiz-Mat. Nauki, 2012, no. 2, pp. 85–92.

    Article  MATH  Google Scholar 

  20. Gavrilenko, S.L., Shil’ko, S.V., and Vasin, R.A., Characteristics of a Viscoplastic Material in the Couette Flow, Journal of Applied Mechanics and Technical Physics, 2002, vol. 43, no. 3, pp. 439–444.

    Article  MATH  Google Scholar 

  21. Lin, C.C., Note on a Class of Exact Solutions in Magneto-Hydrodynamics, Arch. Ration. Mech. Anal., 1958, vol. 1, no. 1, pp. 391–395.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to S. N. Aristov.

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Original Russian Text© S.N. Aristov, E.Yu. Prosviryakov, 2015, published in Izvestiya VUZ. Aviatsionnaya Tekhnika, 2015, No. 4, pp. 50–54.

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Aristov, S.N., Prosviryakov, E.Y. Large-scale flows of viscous incompressible vortical fluid. Russ. Aeronaut. 58, 413–418 (2015). https://doi.org/10.3103/S1068799815040091

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  • DOI: https://doi.org/10.3103/S1068799815040091

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