Structure of quantum vortex tangle in He-4 counterflow turbulence

The main goal of this paper is to present a comprehensive characterization of well developed vortex tangles in a turbulent counterflow in quantum fluids (with a laminar normal fluid component). We analyze extensive numerical simulations using the vortex filament method, solving the full Biot-Savart equations for the vortex dynamics in a wide range of temperatures and counter-flow velocities. In addition to a detailed analysis of traditional characteristics such as vortex line density, anisotropic and curvature parameters of the vortex tangle, we stress other dynamical and statistical characteristics which are either much less studied or even unstudied. The latter include reconnection rates, mean mutual friction forces, drift velocities and the probability distribution functions of various tangle parameters: the loop length, the line curvature, the mean curvature of loops with a given length, etc. During these studies we compare the three main reconnection procedures which are widely used in the literature, and identify which properties are strongly affected by the choice of the reconnection criteria and which of them are practically insensitive to the reconnection procedure. The conclusion is that the vortex filament method in the framework of the Biot-Savart equation sufficiently robust and well suited for the description of the steady state vortex tangle in a quantum counterflow. The Local-Induction Approximation to this equation may be successfully used to analytically establish relationships between mean characteristics of the stochastic vortex tangle.