Advertisement

Journal of Low Temperature Physics

, Volume 145, Issue 1–4, pp 125–142 | Cite as

Energy Spectra of Developed Turbulence in Helium Superfluids

  • V. S. L’vov
  • S. V. Nazarenko
  • L. Skrbek
Universal Features in Turbulence: From Quantum to Cosmological Scales

We suggest a “minimal model” for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier–Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to the temperature dependent parameter q = α/(1 + α′), where α and α′ denote the dimensionless parameters characterizing the mutual friction between quantized vortices and the normal component of the liquid. We then derive the energy balance equations, taking into account the cross-velocity correlations. We obtain all asymptotical solutions for normal and superfluid energy spectra for limiting cases of small/big normal to superfluid density ratio and coupling. We discuss the applicability of our model to superfluid He II and to 3He-B.

PACS Numbers

67.40.Vs 67.57.De 47.27.Ak 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vinen W.F., Niemela J J., (2002) . J. Low Temp. Phys. 128, 167CrossRefGoogle Scholar
  2. 2.
    Vinen W F., Proc. Royal Soc. A240 114, 128 (1957); A242 489 (1957); A242, 493 (1957).Google Scholar
  3. 3.
    Skrbek L., Niemela J.J., Sreenivasan K.R., (2001) . Phys. Rev. E 64: 067301CrossRefADSGoogle Scholar
  4. 4.
    Bradley D.I., Clubb D.O., Fisher S.N., Guénault A.M., Haley R.P., Matthews C.J., Pickett G.R., Tsepelin V., Zaki K., (2005) . Phys. Rev. Lett. 95, 035302CrossRefADSGoogle Scholar
  5. 5.
    Araki T., Tsubota M., Nemirovskii S.K., (2002) . Phys. Rev. Lett. 89: 145301CrossRefADSGoogle Scholar
  6. 6.
    Nore C., Abid M., Brachet M.E., (1997) . Phys. Fluids 9: 2644CrossRefADSMathSciNetzbMATHGoogle Scholar
  7. 7.
    Kobayashi M., Tsubota M., (2005) . Phys. Rev. Lett. 94: 065302CrossRefADSGoogle Scholar
  8. 8.
    Maurer J., Tabeling P., (1998) . Europhys. Lett. 43, 29CrossRefADSGoogle Scholar
  9. 9.
    Volovik G E., JETP Letters 78, 533 (2003); J. Low Temp. Phys. 136, 309 (2004).Google Scholar
  10. 10.
    Vinen W.F., (2005) . Phys. Rev. B 71: 024513CrossRefADSGoogle Scholar
  11. 11.
    L’vov V.S., Nazarenko S.V., Volovik G.E., (2004) . JETP Lett. 80, 479CrossRefADSGoogle Scholar
  12. 12.
    Skrbek L., (2006) . JETP Lett. 83, 127CrossRefADSGoogle Scholar
  13. 13.
    Donnelly R.J., Barenghi C.F.,(1998) . J. Phys. Chem. Data 27: 1217ADSCrossRefGoogle Scholar
  14. 14.
    Vollhardt D. and P.Völfle, The Superfluid Phases of Helium 3, Taylor and Francis, London (1990).Google Scholar
  15. 15.
    Donnelly R J., Quantized Vortices in Hellium II, Cambridge University Press (1991).Google Scholar
  16. 16.
    Kovasznay L., (1947) . J. Aeronaut. Sci. 15, 745MathSciNetGoogle Scholar
  17. 17.
    Nazarenko S., (2005) . JETP Lett 83, 198CrossRefADSGoogle Scholar
  18. 18.
    Kozik E.V., Svistunov B.V., (2004) . Phys. Rev. Lett. 92: 035301CrossRefADSGoogle Scholar
  19. 19.
    T.D.C. Bevan et al., Nature, 386, 689 (1997); J. Low Temp. Phys, 109, 423 (1997).Google Scholar
  20. 20.
    Stalp S.R., Niemela J.J., Vinen W.F., Donnelly R.J., (2002) . Phys. Fluids 14: 1377CrossRefADSGoogle Scholar
  21. 21.
    Vinen W F., private communication.Google Scholar
  22. 22.
    Tsubota M., Barenghi C.F., Araki T., Mitani A., (2004) . Phys. Rev. B 69: 134515CrossRefADSGoogle Scholar
  23. 23.
    Barenghi C.F., Donnelly R.J., Vinen W.F., (1983) . J. Low Temp. Phys. 52, 189CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • V. S. L’vov
    • 1
  • S. V. Nazarenko
    • 2
  • L. Skrbek
    • 3
    • 4
  1. 1.Department of Chemical PhysicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.University of Warwick, Mathematics InstituteCoventryU.K.
  3. 3.Institute of Physics ASCRPragueCzech Republic
  4. 4.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

Personalised recommendations