On the Hall–Vinen–Bekharevich–Khalatnikov Model in Superfluid Turbulence in He II

A critical analysis of the use of the HVBK method to study three-dimensional, turbulent flows of superfluids is presented. The formalism incorporates mutual friction between the normal and superfluidity velocities due to quantum vortexes. The approach relies on the HVBK model, originally developed for He II rotation. It relates vortex line density to coarse-grain vorticity, using the well-known Feynman’s rule. Various justifications and results associated with the method are analyzed. Particular emphasis is placed on the so-called “vortex bundle” structure. The concept of vortex bundles forming quantum turbulence structure is controversial, and does not support the use of HVBK. The final conclusion is that HVBK seems highly counterproductive because it completely disregards the actual structure of vortex tangle as a chaotic cluster of vortex loops and prevents development of adequate theory.