Structure of a quantum vortex tangle in 4 He counterflow turbulence

The paper presents a comprehensive characterization of well-developed vortex tangles in a turbulent counterflow in quantum fluids (with a laminar normal fluid component). We perform and 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 counterflow velocities. We start with the analysis of the macroscopic characteristics of the quantum vortex tangle such as vortex line density, its mean anisotropic and curvature parameters, the mean friction force between normal and superfluid components, the drift velocity of the vortex tangle, etc. Next we proceed to the main goal of the paper and move from the traditional macroscopic approach in terms of mean characteristics of the vortex tangle to the microscopic statistical and kinetic levels of description of quantum turbulence. These include objects that are much less studied or even totally neglected such as the vortex reconnection rates, the correlations and probability distribution functions (PDFs) of the vortex loop lengths, of the line curvature, of the mean curvatures of individual loops, the cross-correlation function between the loop length and its mean curvature, and the autocorrelation function of the vortex-line orientations. This detailed statistical information is required for a deeper understanding of quantum turbulence and for the development of its advanced theoretical description. In addition, we identify which of the studied properties are strongly affected by the choice of the reconnection criteria that are traditionally used in the vortex filament method and which of them are practically insensitive to the reconnection procedure. We conclude that the vortex filament method is sufficiently robust and well-suited for the description of the steady-state vortex tangle in the quantum counterflow.