Fluid Dynamics

, Volume 53, Issue 1, pp 127–135 | Cite as

Numerical Modeling of Two-Dimensional Flow of a Nonhomogeneous Fluid in a Confined Domain

  • S. F. Garanin
  • E. M. Kravets
  • O. N. Pronina
  • A. L. Stadnik


The pattern of the two-dimensional vortex flow of a nonhomogeneous fluid in a confined domain is studied using two-dimensional numerical calculations. It is found that in the case of a nonhomogeneous initial density distribution the kinetic energy decay rates are proportional to the square root of viscosity at the active stage of flow restructuring. The correlation functions of the velocity and the density are derived for different moments of time in the inertial range. All these results indicate the choice of the two-dimensional turbulence development scenario in a nonhomogeneous fluid.

Key words

two-dimensional turbulence Rayleigh–Taylor instability 


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  1. 1.
    A. P. Mirabel’ and A. S. Monin, “Two-Dimensional Turbulence,” Usp. Mekhaniki 2 (3), 47 (1979).MathSciNetGoogle Scholar
  2. 2.
    A. M. Buyko, V. K. Chernyshev, V. A. Demidov, Y. N. Dolin, S. F. Garanin, V. A. Ivanov, V. P. Korchagin, M. V. Lartsev, V. I. Mamyshev, A. P. Mochalov, V. N. Mokhov, I. V. Morozov, N. N. Moskvichev, S. V. Pak, E. S. Pavlovsky, S. V. Trusillo, G. I. Volkov, V. B. Yakubov, and V. V. Zmushko, “Investigations of Thermonuclear Magnetized Plasma Generation in the Magnetic Implosion System MAGO,” in: K. Prestwich and W. Baker (Eds.), Digest of Technical Papers: Proc. IX IEEE Intern. Pulsed Power Conf., Vol. 1 (IEEE, New York, 1993), p.156.Google Scholar
  3. 3.
    I. R. Lindemuth, R. E. Reinovsky, R. E. Chrien, J. M. Christian, C. A. Ekdahl, J. H. Goforth, R. C. Haight, G. Idzorek, N. S. King, R. C. Kirkpatrick, R. E. Larson, G. L. Morgan, B. W. Olinger, H. Oona, P. T. Sheehey, J. S. Shlachter, R. C. Smith, L. R. Veeser, B. J. Warthen, S. M. Younger, V. K. Chernyshev, V. N. Mokhov, A. N. Demin, Y. N. Dolin, S. F. Garanin, V. A. Ivanov, V. P. Korchagin, O. D. Mikhailov, I. V. Morozov, S. V. Pak, E. S. Pavlovskii, N. Y. Seleznev, A. N. Skobelev, G. I. Volkov, and V. B. Yakubov, “Target Plasma Formation forMagnetic Compression/Magnetized Target Fusion (MAGO/MTF),” Phys. Rev. Lett. 75 (10), 1953 (1995).ADSCrossRefGoogle Scholar
  4. 4.
    S. F. Garanin, V. I. Mamyshev, and V.B. Yakubov, “The MAGO System: Current Status,” IEEE Trans. Plasma Sci. 34 (5), 2273 (2006).ADSCrossRefGoogle Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Oxford, Pergamon, 1987).zbMATHGoogle Scholar
  6. 6.
    R. H. Kraichnan, “Inertial Ranges in Two-Dimensional Turbulence,” Phys. Fluids 10 (7), 1417 (1967).ADSCrossRefGoogle Scholar
  7. 7.
    M. Chertkov, “Phenomenology of Rayleigh–Taylor Turbulence,” Phys. Rev. Lett. 91 (11), 115001(1-4) (2003).ADSCrossRefGoogle Scholar
  8. 8.
    Yu. V. Yanilkin, S. P. Belyaev, A. V. Gorodnichev, E. G. Voronov, A. R. Guzhova, L. I. Degtyarenko, G. V. Zharova, P. A. Kucherova, A. L. Stadnik, and N. A. Khovrin, “EGAK++ Software Package for Modeling on Adaptively Built-in Fractional Computation Grids,” VANT. Ser.MMTF, issue 1, 20 (2003).Google Scholar
  9. 9.
    S. F. Garanin, E. M. Kravets, O. N. Pronina, and A. L. Stadnyuk, “Two-Dimensional Vortex Flow in a Confined Domain,” in: Young Researchers in the Science. Reports of 13th Scientific and Engineering, Conf. Sarov, October 28–30, 2014 [in Russian] (Sarov, 2015), p.49.Google Scholar
  10. 10.
    P. G. Frik, Turbulence: Approaches and Models [in Russian] (Moscow and Izhevsk, 2010).Google Scholar
  11. 11.
    S. F. Garanin, O. A. Amelicheva, O.M. Burenkov, G. G. Ivanova, and V. N. Sofronov, “Relaxation of a Two-Dimensional MHD Flow across a Magnetic Field (Two-Dimensional Hydrodynamic Flow) in a Confined Domain,” Zh. Eksp. Teor. Fiz. 124, issue 1(17), 70 (2003).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • S. F. Garanin
    • 1
  • E. M. Kravets
    • 1
  • O. N. Pronina
    • 1
  • A. L. Stadnik
    • 1
  1. 1.Research Institute of Experimental PhysicsRussian Federal Nuclear CenterSarov, Nizhny Novgorod oblastRussia

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