G. Volovik and N. Kopnin.
Recent ROTA experiments demonstrated new phenomenon in superfluid turbulence. We analyzed this turbulent state and conditions under which it arises, and found that this represents a new class of turbulence which can shed light on the phenomenon of turbulence in general. It appears that superfluid turbulence is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the relative value of the friction force acting on a vortex with respect to the non-dissipative forces. The inverse parameter 1/q plays the same role as the Reynolds number Re = UR/_ in classical hydrodynamics. It marks the transition between the laminar and turbulent regimes of vortex dynamics. The developed turbulence occurs in superfluids at q << 1, and it is characterized by a logarithmically modified Kolmogorov cascade. Another parameter of superfluid turbulence is the superfluid Reynolds number Res = UR/_, which contains the circulation quantum __characterizing quantized vorticity in superfluids. The two parameters q and Res control the crossover or transition between two classes of superfluid turbulence: (i) The classical regime, where a logarithmically modified Kolmogorov cascade is effective, vortices are locally polarized, and the quantization of vorticity is not important; and (ii) The Vinen quantum turbulence where the properties are determined by the quantization of vorticity. The phase diagram of these dynamical vortex states is suggested.