Classical and quantum regimes of the superfluid turbulence

TL;DR

This paper explores the governing parameters of superfluid turbulence, identifying two key dimensionless numbers that determine the transition between classical and quantum turbulence regimes, and proposes a phase diagram for vortex states.

Contribution

It introduces a framework with two dimensionless parameters to describe superfluid turbulence and delineates the transition between classical and quantum vortex regimes.

Findings

Superfluid turbulence is governed by parameters q and Re_s.

Transition between classical and quantum turbulence is characterized by these parameters.

A phase diagram of vortex states is proposed.

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 1/q playing 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 Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re_s=UR/\kappa, which contains the circulation quantum \kappa 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; and (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.