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VOLUME 78 (2003) | ISSUE 9 | PAGE 1021
Classical and quantum regimes of the superfluid turbulence
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 {\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  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. The phase diagram of the dynamical vortex states is suggested.