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Journal of Low Temperature Physics

, Volume 145, Issue 1–4, pp 89–106 | Cite as

Transition to Superfluid Turbulence

  • V. B. Eltsov
  • M. Krusius
  • G. E. Volovik
Universal Features in Turbulence: From Quantum to Cosmological Scales

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction—the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of \(1/q \lesssim 1\) the dynamics is vortex number conserving, while at low friction and large \(1/q > rsim 1\) vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of 3He-A and 3He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin–Helmholtz instability.

Keywords

quantized vortex vortex dynamics superfluid turbulence transition to turbulence mutual friction instability 

PACS numbers

47.37 67.40 67.57 

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References

  1. 1.
    Feynman R.P, in Progress Low Temperature Physics, Vol. I, Chap. 2, C. J. Gorter (ed.), North-Holland Publ. Co., Amsterdam (1955).Google Scholar
  2. 2.
    Vinen W.F, in Progress Low Temperature Physics, Vol.III, Chap. 1, C. J. Gorter (ed.), North-Holland Publ. Co., Amsterdam (1961).Google Scholar
  3. 3.
    Finne A.P, Araki T, Blaauwgeers R, Eltsov V.B, Kopnin N.B, Krusius M, Tsubota M, Volovik G.E, (2003) . Nature 424: 1022CrossRefADSGoogle Scholar
  4. 4.
    Hof B, Juel A, and Mullin T, Phys. Rev. Lett. 91, 24452 (2003); T. Mullin and J. Low Temp. Phys. (2006), this issue.Google Scholar
  5. 5.
    Finne A.P, Boldarev S, Eltsov V.B, Krusius M, (2004) . J. Low Temp. Phys. 136, 249CrossRefGoogle Scholar
  6. 6.
    Vinen W.F, J. Low Temp. Phys. (2006), this issue.Google Scholar
  7. 7.
    Finne A.P, Boldarev S, Eltsov V.B, Krusius M, (2004) . J. Low Temp. Phys. 135, 479CrossRefGoogle Scholar
  8. 8.
    Solntsev R.E, R. de Graaf, Eltsov V.B, R. Hänninen, and Krusius M, in Proc. Quantum Fluids and Solids Conf. 2006, J. Low Temp. Phys. (2007), cond-mat/0607323.Google Scholar
  9. 9.
    Finne A.P, Eltsov V.B, Eska G, Hänninen R., Kopu J, Krusius M, Thuneberg E.V, Tsubota M, (2006) . Phys. Rev. Lett. 96: 085301CrossRefADSGoogle Scholar
  10. 10.
    Kopnin N.B, (2001). Theory of Nonequilibrium Superconductivity. Clarendon Press, OxfordGoogle Scholar
  11. 11.
    Volovik G.E, (2003). The Universe in a Helium Droplet. Clarendon Press, OxfordMATHGoogle Scholar
  12. 12.
    Combescot R, J. Low Temp. Phys. (2006), this issue.Google Scholar
  13. 13.
    V. S. L’vov, Nazarenko S.V, and Volovik G.E, JETP Lett. 80, 479 (2004); W.F. Vinen, Phys. Rev. B71, 24513 (2005).Google Scholar
  14. 14.
    V. S. L’vov, Nazarenko S.V, and Skrbek L, J. Low Temp. Phys. (2006), this issue, nlin.CD/0606002.Google Scholar
  15. 15.
    Volovik G.E, J. Low Temp. Phys. (2006), this issue, gr-qc/0603093.Google Scholar
  16. 16.
    See also a more extensive review in preparation: A.P. Finne, V.B. Eltsov, R. Hänninen, N.B. Kopnin, J. Kopu, M. Krusius, M. Tsubota and G.E. Volovik, Rep. Prog. Phys. (2006), cond-mat/0606619.Google Scholar
  17. 17.
    Lord Kelvin (Sir William Thomson), Mathematical and Physical Papers, Vol. 4, Hydrodynamics and General Dynamics, Cambridge University Press, Cambridge (1910).Google Scholar
  18. 18.
    Lord Rayleigh (J.W. Strutt), Scientific Papers, Vol. 1, Cambridge University Press, Cambridge, (1899).Google Scholar
  19. 19.
    Landay L.D., Lifshitz E.M, (1987). Fluid Mechanics, 2nd edn. Pergamon Press, Oxford, UKGoogle Scholar
  20. 20.
    Volovik G.E, JETP Lett. 75, 418 (2002); JETP Lett. 76, 240 (2002).Google Scholar
  21. 21.
    Abanin D.A, (2003) . JETP Lett. 77, 191CrossRefADSGoogle Scholar
  22. 22.
    Blaauwgeers R, Eltsov V.B, Eska G, Finne A.P, Haley R.P, Krusius M, Ruohio J.J, Skrbek L, Volovik G.E, (2002) . Phys. Rev. Lett. 89: 155301CrossRefADSGoogle Scholar
  23. 23.
    Ruokola T., Kopu J, (2005) . JETP Lett. 81, 634CrossRefGoogle Scholar
  24. 24.
    Schützhold R., Unruh W.G, (2002) . Phys. Rev. D 66: 044019CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    M. Abid and Verga A, physics/0607108.Google Scholar
  26. 26.
    Hänninen R., Blaauwgeers R, Eltsov V.B, Finne A.P, Krusius M, Thuneberg E.V, Volovik G.E, (2003) . Phys. Rev. Lett. 90: 225301CrossRefADSGoogle Scholar
  27. 27.
    Bevan T.D.C., Manninen A.J, Cook J.B, Alles H, Hook J.R., Hall H.E, (1997) . J. Low Temp. Phys. 109, 423Google Scholar
  28. 28.
    Sonin E.B, (1987) . Rev. Mod. Phys. 59, 87CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    Skrbek L, (2004) . JETP Lett. 80, 484CrossRefGoogle Scholar
  30. 30.
    Eltsov V.B, Blaauwgeers R, Kopnin N.B, Krusius M, Ruohio J.J, Schanen R, Thuneberg E.V, (2002). Phys. Rev. Lett. 88: 065301CrossRefADSGoogle Scholar
  31. 31.
    V. M. H. Ruutu, Kopu J, Krusius M, Ü. Parts, B. Plaçais, Thuneberg E.V, and Xu W, Phys. Rev. Lett. 79, 5058 ((1997); J. Kopu and Thuneberg E.V, Phys. Rev. B62, 12374 (2000).Google Scholar
  32. 32.
    Tsubota M, Araki T, and C.F. Barenghi, Phys. Rev. Lett. 90, 205301 (2003). Based on measurements by: C.E. Swanson, C.F. Barenghi, and R.J. Donnelly, Phys. Rev. Lett. 50, 190 (1983).Google Scholar
  33. 33.
    Eltsov V.B, Finne A.P, Hänninen R., Kopu J, Krusius M, Tsubota M., Thuneberg E.V, (2006) . Phys. Rev. Lett. 96: 215302CrossRefADSGoogle Scholar
  34. 34.
    Finne A.P, Eltsov V.B, Blaauwgeers R, Krusius M, Janu Z, Skrbek L, (2004) . J. Low Temp. Phys. 134, 375CrossRefGoogle Scholar
  35. 35.
    R. M. Ostermeyer and W.I. Glaberson, J. Low Temp. Phys. 21, 191 (1975); Phys. Rev. Lett. 33, 1197 (1974).Google Scholar
  36. 36.
    Kobayashi M., Tsubota M, (2006) . Phys. Rev. Lett. 97: 145301CrossRefADSGoogle Scholar
  37. 37.
    N. G. Parker and Adams C.S, Phys. Rev. Lett. 95, 145301 (2005); V. Schweikhard, I. Coddington, P. Engels, S. Tung, and Cornell E.A, Phys. Rev. Lett. 93, 210403 (2004).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHutFinland
  2. 2.Kapitza Institute of Physical ProblemsMoscowRussia
  3. 3.Landau Institute for Theoretical PhysicsMoscowRussia

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