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
Abstract
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
in classical
hydrodynamics, and
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.