Influence of different mutual friction models on two-way coupled quantized vortices and normal fluid in superfluid $^4$He

TL;DR

This study compares two mutual friction models in superfluid helium-4 simulations, showing that the self-consistent two-way coupled model better captures vortex dynamics at microscopic scales, while the simpler model suffices for complex flows.

Contribution

It provides a detailed comparison of two mutual friction models, highlighting their respective advantages and limitations in simulating superfluid vortex dynamics.

Findings

S2W model better captures vortex ring propagation and reconnection.

2W model can be used at lower resolution for complex flows.

Both models exhibit -3 power-law tails in velocity fluctuation PDFs.

Abstract

We study the influence of two mutual friction models on quantized vortices and normal fluid using two-way coupled simulations of superfluid $^4$He. The normal fluid is affected by quantized vortices via mutual friction. A previous study [Y. Tang, et al. Nat. Commun. 14, 2941 (2023)] compared the time evolutions of the vortex ring radius and determined that the self-consistent two-way coupled mutual friction (S2W) model yielded better agreement with the experimental results than the two-way coupled mutual friction (2W) model whose model parameters were determined through experiments with rotating superfluid helium. In this study, we compare the two models in more detail in terms of the quantized vortex ring propagation, reconnection, and thermal counterflow. We show that the S2W model exhibits better results than the 2W model on the microscopic scale near a quantized vortex, such as during quantized vortex ring propagation and reconnection, although the S2W model requires a higher spatial resolution. For complex flows such as a thermal counterflow, the 2W model can be applied even to a low-resolution flow while maintaining the anisotropic normal fluid velocity fluctuations. In contrast, the 2W model predicts lower normal fluid velocity fluctuations than the S2W model. The two models show probability density functions with $- 3$ power-law tails for the normal fluid velocity fluctuations.