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 1/q plays the same role as the Reynolds number Re=UR/\nu 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. Another parameter of superfluid turbulence is the superfluid Reynolds number Re_s=UR/\kappa, which contains the circulation quantum \kappa characterizing quantized vorticity in superfluids. The two parameters q and Re_s control the crossover or transition between two classes of superfluid turbulence: (i) the classical regime, where the Kolmogorov cascade (probably modified by the non-canonical dissipation due to mutual friction) 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.