Dynamics of the vortex line density in superfluid counterflow turbulence

TL;DR

This paper develops a minimal closure model for the vortex line density in superfluid counterflow turbulence, incorporating an anisotropy parameter, and validates it through numerical simulations.

Contribution

It introduces a novel minimal closure model for vortex line density in superfluid turbulence using an additional anisotropy parameter, tested against simulations.

Findings

Closure equations accurately predict vortex line density evolution.

Model captures effects of anisotropy in superfluid turbulence.

Predictions agree with numerical simulation results.

Abstract

Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\cal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\cal{L}$ and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter $I_{l0}$. Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter $I_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.