Fully Coupled Two-Fluid Dynamics in Superfluid $^4$He: Anomalous Anisotropic Velocity Fluctuations in Counterflow

TL;DR

This paper presents a numerical simulation of the fully coupled two-fluid dynamics in superfluid helium-4, revealing anisotropic velocity fluctuations in counterflow that align with experimental observations.

Contribution

It introduces a comprehensive 3D fully coupled simulation of superfluid and normal fluid dynamics, confirming experimental findings of anisotropic velocity fluctuations.

Findings

Streamwise fluctuations are more intense and correlated over longer distances.

Simulation results agree with recent visualization experiments.

The model successfully explains anisotropic velocity fluctuations in superfluid counterflow.

Abstract

We investigate the thermal counterflow of the superfluid $^4$He by numerically simulating three-dimensional fully coupled dynamics of the two fluids, namely quantized vortices and a normal fluid. We analyze the velocity fluctuations of the laminar normal fluid arising from the mutual friction with the quantum turbulence of the superfluid component. The streamwise fluctuations exhibit higher intensity and longer-range autocorrelation, as compared to transverse ones. The anomalous fluctuations are consistent with visualization experiments [Mastracci et al., Phys. Rev. Fluids, Vol. 4, 083305 (2019)], and our results confirm their analysis with simple models on the anisotropic fluctuations. This success validates the model of the fully coupled dynamics and paves the way for solving some outstanding problems in this two-fluid system.