Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence

TL;DR

This paper extends the Vinen equation for vortex line density in rotating superfluid turbulence to non-collinear counterflow and analyzes it through non-equilibrium thermodynamics, revealing the role of anisotropy and rotation rate.

Contribution

It introduces a new extended evolution equation for vortex line density considering non-collinear counterflow and rotation, analyzed via non-equilibrium thermodynamics.

Findings

The extended equation accounts for anisotropy in the vortex tangle.

Compatibility with superfluid velocity evolution requires a new anisotropy-dependent term.

The friction force depends on the rotation rate as indicated by the new term.

Abstract

In two previous papers two evolution equations for the vortex line density $L$, proposed by Vinen, were generalized to rotating superfluid turbulence and compared with each other. Here, the already generalized alternative Vinen equation is extended to the case in which counterflow and rotation are not collinear. Then, the obtained equation is considered from the viewpoint of non-equilibrium thermodynamics. According with this formalism, the compatibility between this evolution equation for $L$ and that one for the velocity of the superfluid component is studied. The compatibility condition requires the presence of a new term dependent on the anisotropy of the tangle, which indicates how the friction force depends on the rotation rate.