Abstract
The hydrodynamic problems of superfluid fluid containing chaotic tangles of quantized vortex filaments are discussed. The construction of such hydrodynamics crucially depends on the statistics of vortex tangles, and two important cases are presented. The first corresponds to a tangle that consists of entirely chaotic vortex filaments. This case is implemented in counterflowing helium, and is referred to as Vinen turbulence. In the construction of macroscopic dynamics, the system of equations is closed by the Vinen equation for the density of vortex filaments. The second, referred to as the Hall–Vinen–Bekarevich–Khalatnikov case, corresponds to a situation where the system contains bundles of polarized vortex filaments. In this instance, the system is closed by the Feynman equation that relates density of vortex filaments with the vorticity of superfluid velocity. Problems related to the application of both approaches are discussed.
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