Advertisement

Folding in Two-dimensional Hydrodynamic Turbulence

  • E. A. KuznetsovEmail author
  • E. V. Sereshchenko
Article

Abstract

The vorticity rotor field B = rot ω (divorticity) for freely decaying two-dimensional hydrodynamic turbulence due to a tendency to breaking is concentrated in the vicinity of the lines corresponding to the position of the vorticity quasi-shocks. The maximum value of the divorticity Bmax at the stage of quasishocks formation increases exponentially in time, while the thickness (t) of the maximum area in the transverse direction to the vector B decreases in time also exponentially. It is numerically shown that Bmax(t) depends on the thickness according to the power law: Bmax(t) ~ −α(t), where the exponent α ≈ 2/3. This behavior indicates in favor of folding for the divergence-free vector field of the divorticity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Phys 19, 105110 (2007).Google Scholar
  2. 2.
    E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Theor 24, 253 (2010).Google Scholar
  3. 3.
    A. N. Kudryavtsev, E. A. Kuznetsov, and E. V. Sereshchenko, JETP 96, 699 (2013).CrossRefGoogle Scholar
  4. 4.
    E. A. Kuznetsov and E. V. Sereshchenko, JETP 102, 760 (2015).CrossRefGoogle Scholar
  5. 5.
    R. Kraichnan, Phys 11, 1417 (1967).Google Scholar
  6. 6.
    E. A. Kuznetsov and E. V. Sereshchenko, JETP 105, 83 (2017).CrossRefGoogle Scholar
  7. 7.
    E. A. Kuznetsov and V. P. Ruban, JETP 67, 1076 (1998).CrossRefGoogle Scholar
  8. 8.
    E. A. Kuznetsov and V. P. Ruban, Phys 61, 831 (2000).Google Scholar
  9. 9.
    S. F. Shandarin and Ya. B. Zeldovich, Rev 61, 185 (1989).Google Scholar
  10. 10.
    V. I. Arnold, Catastrophe Theory, 3-rd ed., Springer-Verlag, Berlin (1992).CrossRefGoogle Scholar
  11. 11.
    D. S. Agafontsev, E. A. Kuznetsov, and A. A. Mailybaev, Phys 30, 095104 (2018).Google Scholar
  12. 12.
    D. S. Agafontsev, E. A. Kuznetsov, and A. A. Mailybaev, Phys 27, 085102 (2015).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.L. D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia
  4. 4.Far-Eastern Federal UniversityVladivostokRussia
  5. 5.S. A. Khristianovich Institute of Theoretical and Applied MechanicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

Personalised recommendations