Structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids and in a Bose – Einstein condensate

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluid liquids and in a Bose – Einstein condensate in the presence of a counterflow of normal and superfluid components, we investigate the structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids. Using the characteristic functional method, the properties of hydrodynamic vortex filaments are examined. It is shown that the average curvature of the vortex lines is on the order of the intervortex distance, with the proportionality coefficient being independent of the counterflow velocity. It is found that the degree of anisotropy of the vortex loops does not depend on the applied counterflow velocity. The obtained results explain the origin of the anisotropy as well as the relationship between the curvature of the lines and the intervortex space and their dependence on the parameters of the problem.