Quantum turbulence at finite temperature: the two-fluids cascade

TL;DR

This paper presents DNS simulations of quantum turbulence in superfluid helium, revealing strong fluid locking, scale-dependent force balances, and a temperature-dependent energy relation, advancing understanding of quantum turbulence dynamics.

Contribution

The study introduces detailed DNS analysis of coupled superfluid and normal fluid dynamics, highlighting fluid locking and deriving a superfluid energy relation, which are novel insights in quantum turbulence modeling.

Findings

Strong locking of superfluid and normal fluid across scales

Derivation of a temperature-dependent energy relation

Insights into force balances and effective viscosity

Abstract

To model isotropic homogeneous quantum turbulence in superfluid helium, we have performed Direct Numerical Simulations (DNS) of two fluids (the normal fluid and the superfluid) coupled by mutual friction. We have found evidence of strong locking of superfluid and normal fluid along the turbulent cascade, from the large scale structures where only one fluid is forced down to the vorticity structures at small scales. We have determined the residual slip velocity between the two fluids, and, for each fluid, the relative balance of inertial, viscous and friction forces along the scales. Our calculations show that the classical relation between energy injection and dissipation scale is not valid in quantum turbulence, but we have been able to derive a temperature--dependent superfluid analogous relation. Finally, we discuss our DNS results in terms of the current understanding of quantum turbulence, including the value of the effective kinematic viscosity.