Journal of Low Temperature Physics

, Volume 136, Issue 5–6, pp 309–327 | Cite as

On Developed Superfluid Turbulence

  • G.E. Volovik


Superfluid turbulence is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the relative value of the friction force acting on a vortex with respect to the non-dissipative forces. The inverse parameter q−1 plays the same role as the Reynolds number Re = U R/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence, described by a Kolmogorov cascade, occurs when Re ≪ 1 in classical hydrodynamics. In superfluids, the developed turbulence occurs at q ≪ 1. Another parameter of superfluid turbulence is the superfluid Reynolds number Res = U R/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. The two parameters q and Res control the crossover or transition between two classes of superfluid turbulence: (i) the classical regime, where the Kolmogorov cascade, probably modifed by the non-canonical dissipation due to mutual friction, is effective, vortices are locally polarized, and the quantization of vorticity is not important; and (ii) the Vinen quantum turbulence where the properties are determined by the quantization of vorticity. The phase diagram of these dynamical vortex states is suggested. PACS numbers: 43.37.+q, 47.32.Cc, 67.40.Vs, 67.57.Fg.


Vortex Phase Diagram Reynolds Number Vorticity Magnetic Material 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.P. Finne, T. Araki, R. Blaauwgeers, V.B. Eitsov, N.B. Kopmn, M. Krusius, L. Skrbek, M. Tsubota, and G.E. Volovik, Nature 424, 1022–1025 (2003).Google Scholar
  2. 2.
    W.F. Vinen, Proc. R. Sac. London A242, 493 (1957).Google Scholar
  3. 3.
    W.F. Vinen, and J.J. Niemela, J. Low Temp. Phys. 128, 167 (2002).Google Scholar
  4. 4.
    W.F. Vinen, to be published in Phys. Rev. B. Google Scholar
  5. 5.
    N.B. Kopnm, to be published in Phys. Rev. Lett.' cond-mat/0309708.Google Scholar
  6. 6.
    G.E. Volovik, Pis'ma Zh. Exp. Tear. Fiz. 78, 1021–1025 (2003) JETP Lett. 78533–537 (2003)].Google Scholar
  7. 7.
    H.E. Hall, in Liquid. Helium, International School of Physics "Enrico Fermi" Course XXI, G. Carreri, ed., Academic Press, New York (1963); Philos. Mag. Supplement 9, issue 33, 89 (1960).Google Scholar
  8. 8.
    E.B. Sonin, Rev. Mod. Phys. 59, 87 (1987).Google Scholar
  9. 9.
    N.B. Kopnm, Theory of Nonequilibnum Superconductivity Clarendon Press, Oxford (2001).Google Scholar
  10. 10.
    T.D.C. Bevan et al., Nature 386, 689 (1997); J. Low Temp. Phys. 109 423 (1997).Google Scholar
  11. 11.
    G.E. Volovik, The Universe in a Helium Droplet Clarendon Press, Oxford (2003).Google Scholar
  12. 12.
    W.D. McComb, The Physics of Fluid Turbulence (clarendon Press, Oxford (1990).Google Scholar
  13. 13.
    K.W. Schwarz, Physica B 197, 324 (1994); Numerical experiments on single quantized vortices, preprint.Google Scholar
  14. 14.
    W.F. Vinen, M. Tsubota, and A. Mitani, Phys. Rev. Lett. 91, 135301 (2003).Google Scholar
  15. 15.
    M. Tsubota, T. Araki, and S.K. Nemirovskii, Phys. Rev. B 62, 11751 (2000).Google Scholar
  16. 16.
    T. Damour and A. Vilenkin, Phys. Rev. D 64, 064008 (2001).Google Scholar
  17. 17.
    L. Biferale, M. Cencini, A.S. Lanotte, M. Sbragaglia and F. Toschi, New J. Phys. 637 (2004).Google Scholar
  18. 18.
    C. Leith, Phys. Fluids 10 1409 (1967); Phys. Fluids 11, 1612 (1968).Google Scholar
  19. 19.
    C. Gonnaughton and S. Nazarenko, Phys. Rev. Lett. 92, 044501 (2004).Google Scholar
  20. 20.
    M. Tsubota, K, Kasamatsu, T. Araki, cond-mat/0309364.Google Scholar
  21. 21.
    M, Tsubota, private communication.Google Scholar
  22. 22.
    W.F. Vinen, private communication.Google Scholar
  23. 23.
    G.J. Gorter and J.H. Mellink, Physica 15, 285–304 (1949).Google Scholar
  24. 24.
    G. Toulouse, in Recent Developments in Gauge Theories 331–362 (1979).Google Scholar
  25. 25.
    A.M. Polyakov, in Contemporary Concepts in Physics 3, Harwood Academic, Chur (1987).Google Scholar
  26. 26.
    T.W.B. Kibble, J. Phys. A 9, 1387–1398 (1976).Google Scholar
  27. 27.
    W.H. Zurek, Nature 317, 505 (1985).Google Scholar
  28. 28.
    D.E. Khmelnitekii, JETP Lett. 38, 552 (1983).Google Scholar
  29. 29.
    A.P. Finne, S. Boldarev, V.B. Eitsov and M. Krusius, to be published in J. Low Temp. Phys. cond-mat/0405608.Google Scholar
  30. 30.
    J.-P. Laval, B. Dubrulle, S. Nazarenko, Phys. Fluids 13, 1995–2012 (2001).Google Scholar
  31. 31.
    L. Skrbek, cond-mat/0402301.Google Scholar
  32. 32.
    J.T. Tough, in Prog. in Low Temp. Phys. vol. VIII, North Holland, Amsterdam (1982).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • G.E. Volovik
    • 1
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyMoscowRussia

Personalised recommendations