Quantum Turbulence Coupled with Externally Driven Normal-Fluid Turbulence in Superfluid $^4$He

TL;DR

This study numerically investigates the interaction between quantum turbulence and externally driven normal-fluid turbulence in superfluid helium-4, revealing how the normal fluid influences quantum vortex dynamics and validating the connection to the T2 state.

Contribution

It provides a numerical analysis of coupled quantum and normal-fluid turbulence, demonstrating the normal fluid's role in the T2 state and proposing a theoretical understanding of their relationship.

Findings

NFT enhances QT via mutual friction

Vortex line density follows L^{1/2} ≈ γ V_{ns}

γ matches experimental T2 state data

Abstract

The coupled dynamics of quantum turbulence (QT) and normal-fluid turbulence (NFT) have been a central challenge in quantum hydrodynamics, since it is expected to cause the unsolved T2 state of QT. We numerically studied the coupled dynamics of the two turbulences in thermal counterflow. NFT is driven by external forces to control its turbulent intensity, and the fast multipole method accelerates the calculation of QT. We show that NFT enhances QT via mutual friction. The vortex line density $L$ of the QT satisfies the statistical law $L^{1/2} \approx \gamma V_{ns}$ with the counterflow velocity $V_{ns}$. The obtained $\gamma$ agrees with the experiment of T2 state, validating the idea that the T2 state is caused by NFT. We propose a theoretical insight into the relation between the two turbulences.