Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

An intrinsic velocity-independent criterion for superfluid turbulence

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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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.

References

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

    ADS  CAS  Article  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)

    ADS  MathSciNet  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  Article  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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. E. Volovik.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature01880

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing