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An intrinsic velocity-independent criterion for superfluid turbulence

Nature volume 424, pages 1022–1025 (2003)Cite this article

Abstract

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence1 is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60Tc (where Tc is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence2. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

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Figure 1: Summary of events at high and low temperatures.
Figure 2: NMR absorption spectra before and after vortex-loop injection.
Figure 3: Principle of measurement and phase diagram of turbulent superflow in 3He-B.

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References

  1. Vinen, W. F. & Niemela, J. J. Quantum turbulence. J. Low-Temp. Phys. 128, 167–231 (2002)

    Article  ADS  CAS  Google Scholar 

  2. McComb, W. D. The Physics of Fluid Turbulence 2 (Clarendon, Oxford, 1990)

    Google Scholar 

  3. Sonin, E. B. Vortex oscillations and hydrodynamics of rotating superfluids. Rev. Mod. Phys. 59, 87–155 (1987)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  4. Barenghi, C. F. et al. Thermal excitation of waves on quantized vortices. Phys. Fluids 28, 498–504 (1985)

    Article  ADS  CAS  Google Scholar 

  5. Kopnin, N. B. Theory of Nonequilibrium Superconductivity 271 (Clarendon, Oxford, 2001)

    Google Scholar 

  6. Bevan, T. D. C. et al. Vortex mutual friction in superfluid 3He. J. Low-Temp. Phys. 109, 423–459 (1997)

    ADS  CAS  Google Scholar 

  7. Blaauwgeers, R. et al. Shear flow and Kelvin-Helmholtz instability in superfluids. Phys. Rev. Lett. 89, 155301 (2002)

    Article  ADS  CAS  Google Scholar 

  8. Ostermeier, R. M. & Glaberson, W. I. Instability of vortex lines in the presence of axial normal fluid flow. J. Low-Temp. Phys. 21, 191–196 (1975)

    Article  ADS  CAS  Google Scholar 

  9. Ruutu, V. M. H. et al. Intrinsic and extrinsic mechanisms of vortex formation in superfluid 3He-B. J. Low-Temp. Phys. 107, 93–164 (1997)

    Article  ADS  CAS  Google Scholar 

  10. Ruutu, V. M. H. et al. Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation. Nature 382, 334–336 (1996)

    Article  ADS  CAS  Google Scholar 

  11. Fisher, S. N. et al. Generation and detection of quantum turbulence in superfluid 3He-B. Phys. Rev. Lett. 86, 244–247 (2001)

    Article  ADS  CAS  Google Scholar 

  12. Skrbek, L. et al. Vortex flow in rotating superfluid 3He-B. Physica B 329–333, 106–107 (2003)

    Article  ADS  Google Scholar 

  13. Schwarz, K. W. Three-dimensional vortex dynamics in superfluid 4He: Homogenous superfluid turbulence. Phys. Rev. B 38, 2398–2417 (1988)

    Article  ADS  CAS  Google Scholar 

  14. Tsubota, M. et al. Dynamics of vortex tangle without mutual friction in superfluid 4He. Phys. Rev. B 62, 11751–11762 (2000)

    Article  ADS  CAS  Google Scholar 

  15. Tsubota, M. et al. Rotating superfluid turbulence. Phys. Rev. Lett. 90, 205301 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the EU-IHP ULTI-3, ESF-COSLAB, and ESF-VORTEX programmes. N.B.K. and G.E.V. are grateful to the Russian Foundation for Basic Research and L.S. to the Grant Agency of the Czech Republic. We thank C.F. Barenghi, P.V.E. McClintock and W.F. Vinen for discussions.

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Authors and Affiliations

  1. Low Temperature Laboratory, Helsinki University of Technology, PO Box 2200, FIN-02015, HUT, Finland

    A. P. Finne, R. Blaauwgeers, V. B. Eltsov, N. B. Kopnin, M. Krusius & G. E. Volovik

  2. Department of Physics, Osaka City University, 558-8585, Sumiyoshi-Ku, Osaka, Japan

    T. Araki & M. Tsubota

  3. Kamerlingh Onnes Laboratory, Leiden University, PO Box 9504, 2300 RA, Leiden, The Netherlands

    R. Blaauwgeers

  4. Kapitza Institute for Physical Problems,

    V. B. Eltsov

  5. Landau Institute for Theoretical Physics, Kosygina 2, 119334, Moscow, Russia

    N. B. Kopnin & G. E. Volovik

  6. Joint Low Temperature Laboratory, Institute of Physics ASCR and Charles University, V Holešovičkách 2, 180 00, Prague, Czech Republic

    L. Skrbek

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  1. A. P. Finne
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Correspondence to G. E. Volovik.

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Finne, A., Araki, T., Blaauwgeers, R. et al. An intrinsic velocity-independent criterion for superfluid turbulence. Nature 424, 1022–1025 (2003). https://doi.org/10.1038/nature01880

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