JETP Letters

, Volume 96, Issue 11, pp 699–705 | Cite as

Statistical properties of freely decaying two-dimensional hydrodynamic turbulence

  • A. N. Kudryavtsev
  • E. A. Kuznetsov
  • E. V. Sereshchenko
Article

Abstract

Statistical characteristics of freely decaying two-dimensional hydrodynamic turbulence at high Reynolds numbers are numerically studied. In particular, numerical experiments (with resolution up to 8192 × 8192) provide a Kraichnan-type turbulence spectrum E k k −3. By means of spatial filtration, it is found that the main contribution to the spectrum comes from sharp vorticity gradients in the form of quasi-shocks. Such quasi-singularities are responsible for a strong angular dependence of the spectrum owing to well-localized (in terms of the angle) jets with minor and/or large overlapping. In each jet, the spectrum decreases as k −3. The behavior of the third-order structure function accurately agrees with the Kraichnan direct cascade concept corresponding to a constant enstrophy flux. It is shown that the power law exponents ξ n for higher structure functions grow with n more slowly than the linear dependence, thus indicating turbulence intermittency.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Kraichnan, Phys. Fluids 11, 1417 (1967).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    D. K. Lilly, J. Fluid Mech. 45, 395 (1971).ADSMATHCrossRefGoogle Scholar
  3. 3.
    J. C. McWilliams, J. Fluid Mech. 146, 21 (1984).ADSMATHCrossRefGoogle Scholar
  4. 4.
    S. Kida, J. Phys. Soc. Jpn. 54, 2840 (1985).ADSCrossRefGoogle Scholar
  5. 5.
    M. E. Brachet, M. Meneguzzi, and P. L. Sulem, Phys. Rev. Lett. 57, 683 (1986).ADSCrossRefGoogle Scholar
  6. 6.
    M. E. Brachet, M. Meneguzzi, and P. L. Sulem, J. Fluid Mech. 194, 333 (1988).ADSCrossRefGoogle Scholar
  7. 7.
    R. Benzi, S. Patarnello, and P. Santangelo, Europhys. Lett. 3, 811 (1986).ADSCrossRefGoogle Scholar
  8. 8.
    B. Legras, B. Santangelo, and R. Benzi, Europhys. Lett. 5, 37 (1988); B. Santangelo, R. Benzi, and B. Legras, Phys. Fluids A 1, 1027 (1989).ADSCrossRefGoogle Scholar
  9. 9.
    K. Okhitani, Phys. Fluids A 3, 1598 (1991).ADSCrossRefGoogle Scholar
  10. 10.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Phys. Fluids 19, 105110 (2007).ADSCrossRefGoogle Scholar
  11. 11.
    P. G. Saffman, Stud. Appl. Math. 50, 49 (1971).Google Scholar
  12. 12.
    E. A. Kuznetsov, JETP Lett. 80, 83 (2004).ADSCrossRefGoogle Scholar
  13. 13.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Ras- mussen, Theor. Comput. Fluid Dyn. 24, 253 (2010).MATHCrossRefGoogle Scholar
  14. 14.
    J. Weiss, Physica D 48, 273 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    E. A. Kuznetsov and V. P. Ruban, JETP Lett. 67, 1076 (1998); Phys. Rev. E 61, 831 (2000).ADSCrossRefGoogle Scholar
  16. 16.
    E. A. Kuznetsov, JETP Lett. 76, 346 (2002).ADSCrossRefGoogle Scholar
  17. 17.
    W. Wolibner, Math. Z. 37, 698 (1933); V. I. Yudovich, Zh. Vychisl. Mat. Mat. Fiz. 3, 1032 (1963); T. Kato, Arch. Rat. Mech. Anal. 25, 189 (1967).MathSciNetCrossRefGoogle Scholar
  18. 18.
    H. A. Rose and P. L. Sulem, J. Phys. 39, 441 (1978).MathSciNetCrossRefGoogle Scholar
  19. 19.
    V. Borue and S. A. Orszag, Europhys. Lett. 20, 687 (1995).ADSCrossRefGoogle Scholar
  20. 20.
    C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods (Springer, Heidelberg, 2006).MATHGoogle Scholar
  21. 21.
  22. 22.
    P. R. Spalart, R. D. Moser, and M. M. Rogers, J. Comput. Phys. 96, 297 (1991).MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    G. Boffetta and R. E. Ecke, Ann. Rev. Fluid Mech. 44, 427 (2012).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. N. Kudryavtsev
    • 1
    • 2
  • E. A. Kuznetsov
    • 1
    • 3
    • 4
  • E. V. Sereshchenko
    • 1
    • 2
    • 5
  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  3. 3.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  4. 4.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  5. 5.Far Eastern Federal UniversityVladivostokRussia

Personalised recommendations