JETP Letters

, Volume 107, Issue 3, pp 157–162 | Cite as

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

  • A. V. Orlov
  • M. Yu. Brazhnikov
  • A. A. Levchenko
Plasma, Hydroand Gas Dynamics


The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.


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  1. 1.
    G. Boffetta and R. E. Ecke, Ann. Rev. Fluid Mech. 71, 427 (2012).ADSCrossRefGoogle Scholar
  2. 2.
    L. M. Smith and V. Yakhot, Phys. Rev. Lett. 71, 352 (1993).ADSCrossRefGoogle Scholar
  3. 3.
    R. H. Kraichnan, Phys. Fluids 10, 1417 (1967).ADSCrossRefGoogle Scholar
  4. 4.
    C. E. Leith, Phys. Fluids 11, 671 (1968).ADSCrossRefGoogle Scholar
  5. 5.
    G. K. Batchelor, Phys. Fluids 12, 233 (1969).CrossRefGoogle Scholar
  6. 6.
    J. Sommeria, J. Fluid Mech. 170, 139 (1986).ADSCrossRefGoogle Scholar
  7. 7.
    H. Xia, M. Shats, and G. Falkovich, Phys. Fluids 21, 125101 (2009).ADSCrossRefGoogle Scholar
  8. 8.
    N. Francois, H. Xia, H. Punzmann, and M. Shats, Phys. Rev. Lett. 110, 194501 (2013).ADSCrossRefGoogle Scholar
  9. 9.
    N. Francois, H. Xia, H. Punzmann, S. Ramsden, and M. Shats, Phys. Rev. X 4, 021021 (2014).Google Scholar
  10. 10.
    I. V. Kolokolov and V. V. Lebedev, JETP Lett. 106, 659 (2017).ADSCrossRefGoogle Scholar
  11. 11.
    A. Frishman, J. Laurie, and G. Falkovich, Phys. Rev. Fluids 2, 032602 (2017).ADSCrossRefGoogle Scholar
  12. 12.
    J. Laurie, G. Boffetta, G. Falkovich, I. Kolokolov, and V. Lebedev, Phys. Rev. Lett. 113, 254503 (2014).ADSCrossRefGoogle Scholar
  13. 13.
    I. V. Kolokolov and V. V. Lebedev, Phys. Rev. E 93, 033104 (2016).ADSCrossRefGoogle Scholar
  14. 14.
    I. V. Kolokolov and V. V. Lebedev, J. Fluid Mech. 809, R2–1 (2016).ADSCrossRefGoogle Scholar
  15. 15.
    W. Thieckle and E. J. Stamhuis, J. Open Res. Software 2, 30 (2014).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. V. Orlov
    • 1
    • 2
    • 3
  • M. Yu. Brazhnikov
    • 1
    • 2
  • A. A. Levchenko
    • 1
    • 2
  1. 1.Institute of Solid State PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and Technology (State University)Dolgoprudny, Moscow regionRussia

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