Development of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in three-dimensional space: Topology of vortex surfaces

  • N. A. Inogamov
  • A. M. Oparin
Plasma, Gases


The evolution of the boundary of a liquid during the development of mixing instabilities is studied. The vortex filaments, which transport liquid masses, are generators of the boundary surface. There is a fundamental difference between two-dimensional (2D) and three-dimensional (3D) motions. In the first case the vortices are rectilinear in planar geometry (2Dp) and ring-shaped in axisymmetric geometry (2Da). In the second case the vortices are very complicated. Spatially periodic (“single-mode”) solutions, which are important in mixing theory, are investigated. These solutions describe one-dimensional chains of alternating bubbles and jets in 2Dp geometry and planar (two-dimensional) arrays or lattices of bubbles and jets in 3D geometry. An analytical description is obtained for the basic types of arrays (rectangular, hexagonal, and triangular). The analysis agrees with the results of numerical simulation.

PACS numbers

47.20.−k 47.32.Cc 47.55.Dz 


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  1. 1.
    S. W. Haan, Phys. Fluids B 3, 2349 (1991).CrossRefADSGoogle Scholar
  2. 2.
    N. A. Inogamov, JETP Lett. 55, 521 (1992).ADSGoogle Scholar
  3. 3.
    S. Atzeni, A. Guerrieri, Europhys. Lett. 22, 603 (1993).ADSGoogle Scholar
  4. 4.
    D. L. Youngs, Laser Part. Beams 12, 725 (1994).ADSGoogle Scholar
  5. 5.
    J. F. Haas, I. Galametz, L. Houas et al., Chocs. Num. 14, 15 (1995).Google Scholar
  6. 6.
    R. L. Holmes, J. W. Grove, and D. H. Sharp, J. Fluid Mech. 301, 51 (1995).ADSMathSciNetGoogle Scholar
  7. 7.
    N. A. Inogamov, Zh. Éksp. Teor. Fiz. 107, 1596 (1995) [JETP 80, 890 (1995)].Google Scholar
  8. 8.
    U. Alon, J. Hecht, D. Ofer, and D. Shvarts, Phys. Rev. Lett. 74, 534 (1995).CrossRefADSGoogle Scholar
  9. 9.
    N. A. Inogamov and S. I. Abarzhi, Physica D 87, 339 (1995).CrossRefGoogle Scholar
  10. 10.
    M. M. Marinak, R. E. Tipton, B. A. Remington et al., Inertial Confinement Fusion 5, 168 (1995).Google Scholar
  11. 11.
    N. A. Inogamov, Proceedings of the 6th International Workshop on the Physics of Compressible Turbulent Mixing, edited by G. Jourdan and L. Houas, Institut Universitaire des Systemes Thermiques Industriels, Printed in France by Imprimerie Caractere, Marseille, 1997, 208.Google Scholar
  12. 12.
    N. A. Inogamov, Laser Part. Beams 15, 53 (1997).Google Scholar
  13. 13.
    K. O. Mikaelian, Phys. Rev. Lett. 80, 508 (1998).CrossRefADSGoogle Scholar
  14. 14.
    M. M. Marinak, S. G. Glendinning, R. J. Wallace et al., Phys. Rev. Lett. 80, 4426 (1998).CrossRefADSGoogle Scholar
  15. 15.
    S. I. Abarzhi, Phys. Rev. Lett. 81, 337 (1998).CrossRefADSGoogle Scholar
  16. 16.
    Q. Zhang, Phys. Rev. Lett. 81, 3391 (1998).ADSGoogle Scholar
  17. 17.
    S. I. Anisimov, A. V. Chekhlov, A. Yu. Dem’yanov, and N. A. Inogamov, Russ. J. Comp. Mech. 1, 5 (1993).Google Scholar
  18. 18.
    D. Layzer, Astrophys. J. 122, 1 (1955).ADSMathSciNetGoogle Scholar
  19. 19.
    Yu. M. Davydov and M. S. Panteleev, Zh. Prikl. Mekh. Tekh. Fiz. 1, 117 (1981).Google Scholar
  20. 20.
    T. Yabe, H. Hoshino, and T. Tsuchiya, Phys. Rev. A 44, 2756 (1991).CrossRefADSGoogle Scholar
  21. 21.
    D. L. Youngs, Phys. Fluids A 3, 1312 (1991).CrossRefADSGoogle Scholar
  22. 22.
    X. L. Li, Phys. Fluids 8, 336 (1996).ADSzbMATHGoogle Scholar
  23. 23.
    O. M. Belotserkovskii, Numerical Simulation in the Mechanics of Continuous Media [in Russian] (Fizmatlit, Moscow, 1994).Google Scholar
  24. 24.
    O. M. Belotserkovskii, Numerical Experiments in Turbulence: From Order to Chaos [in Russian] (Nauka, Moscow, 1994).Google Scholar
  25. 25.
    O. M. Belotserkovskii, V. A. Gushchin, and V. N. Kon’shin, Zh. Vychisl. Mat. Mat. Fiz. 27, 594 (1987).MathSciNetGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 1999

Authors and Affiliations

  • N. A. Inogamov
    • 1
  • A. M. Oparin
    • 2
  1. 1.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow RegionRussia
  2. 2.Institute of Computer-Aided DesignRussian Academy of SciencesMoscowRussia

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