A mathematical model of counterflow superfluid turbulence describing heat waves and vortex-density waves

TL;DR

This paper develops a mathematical model for counterflow superfluid turbulence that captures the interaction between vortex density waves and high-frequency second sound, highlighting the transition from diffusive to wave-like behavior.

Contribution

It introduces a set of evolution equations including vortex flux as an independent variable, enabling detailed analysis of vortex density wave propagation in superfluid turbulence.

Findings

Vortex density perturbations can transition from diffusive to propagative behavior.

The model explains the interaction between vortex waves and high-frequency second sound.

Inclusion of vortex flux as an independent variable is crucial for this transition.

Abstract

The interaction between vortex density waves and high-frequency second sound in counterflow superfluid turbulence is examined, incorporating diffusive and elastic contributions of the vortex tangle. The analysis is based on a set of evolution equations for the energy density, the heat flux, the vortex line density, and the vortex flux, the latter being considered here as an independent variable, in contrast to previous works. The latter feature is crucial in the transition from diffusive to propagative behavior of vortex density perturbations, which is necessary to interpret the details of high-frequency second sound.