Applications of Gaussian model of the vortex tangle in the superfluid turbulent HeII

In spite of an appearance of some impressive recent results in understanding of the superfluid turbulence in HeII they fail to evaluate many characteristics of vortex tangle needed for both applications and fundamental study. Early we reported the Gaussian model of the vortex tangle in superfluid turbulent HeII. That model is just trial distribution functional in space of vortex loop configurations constructed on the basis of well established properties of vortex tangle. It is designed to calculate various averages taken over stochastic vortex loop configurations. In this paper we use this model to calculate some important characteristics of the vortex tangle. In particular we evaluate the average superfluid mass current J induced by vortices and the average energy E associated with the chaotic vortex filament.