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JETP Letters

, Volume 102, Issue 11, pp 760–765 | Cite as

Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence

  • E. A. Kuznetsov
  • E. V. Sereshchenko
Nonlinear Phenomena

Abstract

The statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192 × 8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential influence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ~k –4, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum E k = C Kη2/3k–3, where η is the enstrophy flux and the Kraichnan constant C K ≃ 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S 3 L which, as for the isotropic turbulence, gives the same scaling with respect to the separation length R and η, S 3 L = C 3ηR 3, but the average over the angles and time differs from its isotropic value.

Keywords

Vorticity JETP Letter Isotropic Turbulence Inertial Range Spectral Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Kraichnan, Phys. Fluids 11, 1417 (1967).CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    D. K. Lilly, J. Fluid Mech. 45, 395 (1971).CrossRefADSMATHGoogle Scholar
  3. 3.
    J. C. McWilliams, J. Fluid Mech. 146, 21 (1984).CrossRefADSMATHGoogle Scholar
  4. 4.
    S. Kida, J. Phys. Soc. J. 54, 2840 (1985).CrossRefADSGoogle Scholar
  5. 5.
    M. E. Brachet, M. Meneguzzi, and P. L. Sulem, Phys. Rev. Lett. 57, 683 (1986).CrossRefADSGoogle Scholar
  6. 6.
    M. E. Brachet, M. Meneguzzi, and P. L. Sulem, J. Fluid Mech. 194, 333 (1988).CrossRefADSGoogle Scholar
  7. 7.
    R. Benzi, S. Patarnello, and P. Santangelo, Europhys. Lett. 3, 811 (1986).CrossRefADSGoogle Scholar
  8. 8.
    B. Legras, B. Santangelo, and R. Benzi, Europhys. Lett. 5, 37 (1988)CrossRefADSGoogle Scholar
  9. 8a.
    B. Santangelo, R. Benzi, and B. Legras, Phys. Fluids A 1, 1027 (1989).CrossRefADSGoogle Scholar
  10. 9.
    K. Okhitani, Phys. Fluids A 3, 1598 (1991).CrossRefADSGoogle Scholar
  11. 10.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Phys. Fluids 19, 105110 (2007).CrossRefADSGoogle Scholar
  12. 11.
    P. G. Saffman, Stud. Appl. Math. 50, 49 (1971).Google Scholar
  13. 12.
    W. Wolibner, Math. Z. 37, 698 (1933)CrossRefMathSciNetGoogle Scholar
  14. 12a.
    V. I. Yudovich, 3, 1407 (1963)Google Scholar
  15. 12b.
    T. Kato, Arch. Rat. Mech. Anal. 25, 189 (1967).CrossRefGoogle Scholar
  16. 13.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Theor. Comput. Fluid Dyn. 24, 253 (2010).CrossRefMATHGoogle Scholar
  17. 14.
    A. N. Kudryavtsev, E. A. Kuznetsov, and E. V. Sereshchenko, JETP Lett. 96, 699 (2013).CrossRefADSGoogle Scholar
  18. 15.
    E. A. Kuznetsov, JETP Lett. 80, 83 (2004).CrossRefADSGoogle Scholar
  19. 16.
    T. Gotoh, Phys. Rev. E 57, 298491 (1998).CrossRefMathSciNetGoogle Scholar
  20. 17.
    N. Schorghofer, Phys. Rev. E 61, 657277 (2000).Google Scholar
  21. 18.
    E. Lindborg and K. Alvelius, Phys. Fluids 12, 945 (2000).CrossRefADSMATHGoogle Scholar
  22. 19.
    E. Lindborg and A. Vallgren, Phys. Fluids 22, 091704 (2010).CrossRefADSGoogle Scholar
  23. 20.
    U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge Univ. Press, Cambridge, UK, 1995).MATHGoogle Scholar
  24. 21.
    D. Bernard, Phys. Rev. E 60, 618487 (1999).CrossRefGoogle Scholar
  25. 22.
    E. Lindborg, J. Fluid Mech. 388, 259 (1999).CrossRefADSMATHGoogle Scholar
  26. 23.
    V. Yakhot, Phys. Rev. E 60, 5544 (1999).CrossRefADSMathSciNetGoogle Scholar
  27. 24.
    G. Boffetta and R. E. Ecke, Annu. Rev. Fluid Mech. 44, 427 (2012).CrossRefADSMathSciNetGoogle Scholar
  28. 25.
    E. A. Kuznetsov and V. P. Ruban, JETP Lett. 67, 1076 (1998), Phys. Rev. E 61, 831 (2000).CrossRefADSGoogle Scholar
  29. 26.
    E. A. Kuznetsov, JETP Lett. 76, 346 (2002).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  4. 4.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  5. 5.Far-Eastern Federal UniversityVladivostokRussia

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