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An intrinsic velocity-independent criterion for superfluid turbulence


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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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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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).

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