Method of trial distribution function for quantum turbulence

Abstract

Studying quantum turbulence the necessity of calculation the various characteristics of the vortex tangle (VT) appears. Some of "crude" quantities can be expressed directly via the total length of vortex lines (per unit of volume) or the vortex line density L(t) and the structure parameters of the VT. Other more "subtle" quantities require knowledge of the vortex line configurations {s(ξ,t)}. Usually, the corresponding calculations are carried out with the use of more or less truthful speculations concerning arrangement of the VT. In this paper we review other way to solution of this problem. It is based on the trial distribution functional (TDF) in space of vortex loop configurations. The TDF is constructed on the basis of well established properties of the vortex tangle. It is designed to calculate various averages taken over stochastic vortex loop configurations. In this paper we also review several applications of the use this model to calculate some important characteristics of the vortex tangle. In particular we discussed the average superfluid mass current J induced by vortices and its dynamics. We also describe the diffusion-like processes in the nonuniform vortex tangle and propagation of turbulent fronts.