On developed superfluid turbulence

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 q−1 plays 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 a Kolmogorov cascade, occurs when Re ≫ 1 in classical hydrodynamics. In superfluids, the developed turbulence occurs 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/κ, which contains the circulation quantum κ 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 presented. PACS numbers: 43.37.+q, 47.32.Cc, 67.40.Vs, 67.57.Fg