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VOLUME 78 | ISSUE 9 | PAGE 1021
Classical and quantum regimes of the superfluid turbulence
G. E. Volovik
Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland
Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia

PACS: 43.37.+q, 47.32.Cc, 67.40.Vs, 67.57.Fg
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q-1 playing the same role as the Reynolds number {\rm Re}=UR/\nu in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when {\rm Re}\gg 1 in classical hydrodynamics, and q\ll 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number {\rm Re}_s=UR/\kappa, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.

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