Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles

TL;DR

This paper extends the hydrodynamic equations for superfluid vortex tangles to include anisotropy and polarization effects, improving modeling of complex superfluid turbulence scenarios.

Contribution

It generalizes the Hall-Vinen-Bekarevich-Khalatnikov equations by incorporating anisotropy and polarization, along with an evolution equation for vortex line density.

Findings

Enhanced equations for superfluid turbulence modeling

More accurate description of rotating counterflows and turbulence behind objects

Potential for better predictions in superfluid turbulence experiments

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 ${\bf F}_{ns}$ between normal and superfluid components and to the vortex tension force $\rho_s{\bf T}$. These equations are complemented by an evolution equation for the vortex line density $L$, 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.