Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence

TL;DR

This paper investigates the dynamics of vortex-line density in superfluid turbulence, using inhomogeneous channel flow experiments to evaluate and propose a new equation that aligns with observed data.

Contribution

The authors introduce a new inhomogeneous equation for vortex-line density that better fits experimental data than previous models.

Findings

The traditional form of the production term is inconsistent with experimental data.

Inhomogeneous flow experiments effectively distinguish between competing models.

A new equation for vortex-line density is proposed and validated against data.

Abstract

The quantization of vortex lines in superfluids requires the introduction of their density $\C L(\B r,t)$ in the description of quantum turbulence. The space homogeneous balance equation for $\C L(t)$, proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term $\C P$. Attempts to choose the correct one on the basis of time-dependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is excellently suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new inhomogeneous equation for $\C L(\B r,t)$ that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.