We present a comprehensive characterization of well developed quantum vortex tangles in a turbulent counterflow of superfluid He II. Using the vortex filament method with the full Biot-Savart equations for the vortex dynamics, we analyze their macroscopic and microscopic properties in a wide range of temperatures and counterflow velocities.

In particular, we studied the temperature- and counterflow velocity dependencies of the macroscopic characteristics of the tangle such as the vortex line density, the mean curvature, the mean friction force between normal and superfluid components, the drift velocity of the vortex tangle, etc.

For the first time we described in details the microscopic statistical properties of the tangles that include the 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.

Our results pave a way to a deeper understanding of quantum turbulence and for the development of its advanced theoretical description.