On stochastic mixing caused by the Rayleigh-Taylor instability

  • N. A. Inogamov
  • A. M. OparinEmail author
  • A. Yu. Dem’yanov
  • L. N. Dembitskiĭ
  • V. A. Khokhlov
Nonlinear physics


The mixing of contacting substances is considered. The evolution of the mixing layer over a long time period from multimode initial perturbations is investigated numerically in the short-scale and wide-range cases. In the case of a short-scale initiation, the flow is stochastic in the sense that the time of the considered evolution exceeds the period of correlation. The effect of the amplitude of wide-range perturbations on the dynamics of mixing is analyzed. The scale-invariant properties of the spectral and statistical parameters of turbulent mixing are investigated for the first time. The universal spectra characterizing the turbulence mixing in the entire self-similar interval on a unified basis are obtained. The simulation is based on the effective algorithms with high approximating qualities, which have been tested earlier.


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  1. 1.
    D. H. Sharp, Physica D (Amsterdam) 12, 3 (1984).ADSCrossRefGoogle Scholar
  2. 2.
    H.-J. Kull, Phys. Rep. 206, 197 (1991).ADSCrossRefGoogle Scholar
  3. 3.
    N. A. Inogamov, Astrophys. Space Phys. Rev. 10(2), 1 (1999).ADSGoogle Scholar
  4. 4.
    N. A. Inogamov, A. Yu. Dem’yanov, and É. E. Son, Hydrodynamics of Mixing (Mosk. Fiz.-Tekh. Inst., Moscow, 1999).Google Scholar
  5. 5.
    S. Z. Belen’kiĭ and E. S. Fradkin, Tr. Fiz. Inst. Akad. Nauk SSSR 29, 207 (1965).Google Scholar
  6. 6.
    V. E. Neuvazhaev, Prikl. Mekh. Tekh. Fiz., No. 6, 82 (1976).Google Scholar
  7. 7.
  8. 8.
    O. M. Belotserkovskiĭ, Numerical Simulation in Mechanics of Continuous Media (Fizmatlit, Moscow, 1994).zbMATHGoogle Scholar
  9. 9.
    O. M. Belotserkovskiĭ, V. A. Gushchin, and V. N. Kon’shin, Zh. Vychisl. Mat. Mat. Fiz. 27, 594 (1987).Google Scholar
  10. 10.
    O. M. Belotserkovskiĭ and A. M. Oparin, Numerical Experiment in Turbulence: from Order to Chaos (Nauka, Moscow, 2000).zbMATHGoogle Scholar
  11. 11.
    N. A. Inogamov and A. M. Oparin, Zh. Éksp. Teor. Fiz. 116, 908 (1999) [JETP 89, 481 (1999)].Google Scholar
  12. 12.
    Proceedings of the 6th International Workshop on the Physics of Compressible Turbulent Mixing, Ed. by G. Jourdan and L. Houas (Institut Universitaire des Systemes Thermiques Industriels, Marseille, 1997).Google Scholar
  13. 13.
    S. W. Haan, Phys. Rev. A 39(11), 5812 (1989).ADSCrossRefGoogle Scholar
  14. 14.
    S. W. Haan, Phys. Fluids B 3(8), 2349 (1991).ADSCrossRefGoogle Scholar
  15. 15.
    R. D. Richtmyer, Commun. Pure Appl. Math. 13(2), 297 (1960).MathSciNetCrossRefGoogle Scholar
  16. 16.
    E. E. Meshkov, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 151 (1969).Google Scholar
  17. 17.
    S. G. Zaĭtsev, E. V. Lazareva, V. V. Chernukha, and V. M. Belyaev, Dokl. Akad. Nauk SSSR 283(1), 94 (1985) [Sov. Phys. Dokl. 30, 579 (1985)].Google Scholar
  18. 18.
    J. F. Haas and B. Sturtevant, J. Fluid Mech. 181, 41 (1987).ADSCrossRefGoogle Scholar
  19. 19.
    V. B. Rozanov, I. G. Lebo, S. G. Zaĭtsev, et al., Preprint No. 56, FIAN (Lebedev Institute of Physics, Academy of Sciences of USSR, Moscow, 1990).Google Scholar
  20. 20.
    U. Alon, J. Hecht, D. Ofer, and D. Shvarts, Phys. Rev. Lett. 74, 534 (1995).ADSCrossRefGoogle Scholar
  21. 21.
    Mathematical Encyclopedia, Ed. by I. M. Vinogradov (Sovetskaya Éntsiklopediya, Moscow, 1979).zbMATHGoogle Scholar
  22. 22.
    S. I. Anisimov, Ya. B. Zel’dovich, N. A. Inogamov, and M. F. Ivanov, in Shock Waves, Explosions and Detonation, Ed. by M. Summerfield (AIAA, Washington, 1983), Vol. 87, p. 218.Google Scholar
  23. 23.
    N. A. Inogamov, Pis’ma Zh. Tekh. Fiz. 4(12), 743 (1978) [Sov. Tech. Phys. Lett. 4, 299 (1978)].Google Scholar
  24. 24.
    A. M. Prokhorov, S. I. Anisimov, and P. P. Pashinin, Usp. Fiz. Nauk 119(3), 401 (1976) [Sov. Phys. Usp. 19, 547 (1976)].ADSCrossRefGoogle Scholar
  25. 25.
    D. T. Dumitrescu, Z. Angew. Math. Mech. 23(3), 139 (1943).MathSciNetCrossRefGoogle Scholar
  26. 26.
    R. M. Davies and G. I. Taylor, Proc. R. Soc. London, Ser. A 200, 375 (1950).ADSCrossRefGoogle Scholar
  27. 27.
    P. R. Garabedian, Proc. R. Soc. London, Ser. A 241(1226), 423 (1957).ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    G. Birkhoff and D. Carter, J. Math. Mech. 6(6), 769 (1957).MathSciNetGoogle Scholar
  29. 29.
    J.-M. Vanden-Broeck, Phys. Fluids 27(5), 1090 (1984).ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    S. I. Anisimov, A. V. Chekhlov, A. Yu. Dem’yanov, and N. A. Inogamov, Russ. J. Comput. Mech. 1, 5 (1993).Google Scholar
  31. 31.
    G. Birkhoff and E. H. Zarantonello, Jets, Wakes and Cavities (Academic, New York, 1957; Mir, Moscow, 1964).zbMATHGoogle Scholar
  32. 32.
    M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models (Nauka, Moscow, 1970).Google Scholar
  33. 33.
    S. F. Garanin, Vopr. At. Nauki Tekh., Ser.: Teor. Prikl. Fiz., No. 3/1, 12 (1995). (S. F. Garanin, in Proceedings of the 5th International Workshop Compressible Turbulent Mixing, Ed. by D. Youngs, J. Glimm, and B. Boston (World Scientific, Singapore, 1995).)Google Scholar
  34. 34.
    P. Wilson, M. Andrews, and F. Harlow, Phys. Fluids 11(8), 2425 (1999).ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    M. B. Schneider, G. Dimonte, and B. Remington, Phys. Rev. Lett. 80(16), 3507 (1998).ADSCrossRefGoogle Scholar
  36. 36.
    D. L. Youngs, Phys. Fluids A 3(5), 1312 (1991).ADSCrossRefGoogle Scholar
  37. 37.
    K. I. Read, Physica D (Amsterdam) 12(1–3), 45 (1984).ADSCrossRefGoogle Scholar
  38. 38.
    Yu. V. Yanilkin, Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsessov, No. 4, 88 (1999).Google Scholar
  39. 39.
    J. Glimm, J. W. Grove, X.-L. Li, et al., SIAM J. Sci. Comput. (USA) 19, 703 (1998).MathSciNetCrossRefGoogle Scholar
  40. 40.
    N. N. Anuchina, N. S. Es’kov, A. V. Polionov, et al., in Proceedings of the 6th International Workshop on the Physics of Compressible Turbulent Mixing, Ed. by G. Jourdan and L. Houas (Institut Universitaireles Systemes Thermiques Industriels, Marseille, 1997).Google Scholar
  41. 41.
    M. D. Kamchibekov, E. E. Meshkov, N. V. Nevmerzhitskiĭ, and E. A. Sotskov, Preprint No. 46-96, RFYaTs, VNIIÉF (Sarov, 1996).Google Scholar
  42. 42.
    X. He, R. Zhang, S. Chen, and G. D. Doolen, Phys. Fluids 11(5), 1143 (1999).ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    G. Birkhoff, in Proceedings of Symposia in Applied Mathematics, Vol. XIII: Hydrodynamic Instability, Ed. by G. Birkhoff, R. Bellman, and C. C. Lin (American Mathematical Society, 1962; Mir, Moscow, 1964).Google Scholar
  44. 44.
    N. A. Inogamov, Zh. Éksp. Teor. Fiz. 107(5), 1596 (1995) [JETP 80, 890 (1995)].Google Scholar
  45. 45.
    D. L. Youngs, Physica D (Amsterdam) 12(1–3), 32 (1984).ADSCrossRefGoogle Scholar
  46. 46.
    P. F. Linden, J. M. Redondo, and D. L. Youngs, J. Fluid Mech. 265, 97 (1994).ADSCrossRefGoogle Scholar
  47. 47.
    D. Ofer, D. Shvarts, Z. Zinamon, and S. A. Orszag, Phys. Fluids B 4, 3549 (1992).ADSCrossRefGoogle Scholar
  48. 48.
    D. Ofer, U. Alon, D. Shvarts, et al., Phys. Plasmas 3(8), 3073 (1996).ADSCrossRefGoogle Scholar
  49. 49.
    S. I. Voropayev and Y. D. Afanasyev, Phys. Fluids A 5(10), 2461 (1993).ADSCrossRefGoogle Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • N. A. Inogamov
    • 1
  • A. M. Oparin
    • 2
    Email author
  • A. Yu. Dem’yanov
    • 3
  • L. N. Dembitskiĭ
    • 3
  • V. A. Khokhlov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Institute for Computer-Aided DesignRussian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyĭ, Moscow oblastRussia

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