Alternative Vinen's equation and its extension to rotating counterflow superfluid turbulence

TL;DR

This paper compares two alternative Vinen's equations for vortex line density in rotating superfluid turbulence, analyzing their steady and unsteady behaviors against experimental data, and finds the traditional equation fits observations better.

Contribution

It proposes an extension of the alternative Vinen's equation to rotating counterflow superfluid turbulence and compares its predictions with experimental results.

Findings

Traditional Vinen's equation fits experimental data better.

Alternative equations reach steady state faster.

Both equations produce similar steady-state results.

Abstract

Two alternative Vinen's evolution equations for the vortex line density L in counterflow superfluid turbulence, are physically admissible and lead to analogous results in steady states. In Phys. Rev. B, 69, 094513 (2004) the most used of them was generalized to counterflow superfluid turbulence in rotating containers. Here, the analogous generalization for the alternative Vinen's equation is proposed. Both generalized Vinen's equations are compared with the experimental results, not only in steady-states but also in some unsteady situations. From this analysis follows that the solutions of the alternative Vinen's equation tend significantly faster to the corresponding final steady state values than the solutions of the usual Vinen's equation, and that the latter seems more suitable for the description of the experimental available data.