Classical and quantum regimes of superfluid turbulence

  • G. E. Volovik
Nomlinear Dynamics


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 Re=UR/ν 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 Re≫1 in classical hydrodynamics, and q≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Res=UR/κ, 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. A phase diagram of the dynamical vortex states is suggested.

PACS numbers

47.37.+q 47.32.Cc 67.40.Vs 67.57.Fg 


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Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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