Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles
arXiv:0806.1889
Abstract
We include the effects of anisotropy and polarization in the hydrodynamics of inhomogeneous vortex tangles, thus generalizing the well known Hall-Vinen-Bekarevich-Khalatnikov equations, which do not take them in consideration. These effects contribute to the mutual friction force between normal and superfluid components and to the vortex tension force . These equations are complemented by an evolution equation for the vortex line density , which takes into account these contributions. These equations are expected to be more suitable than the usual ones for rotating counterflows, or turbulence behind a cylinder, or turbulence produced by a grid of parallel thin cylinders towed across a superfluid, because in these situations polarization is expected to play a relevant role.
21 pages