Overview
Numerical simulations investigated thermal-counterflow turbulence within a bulk region, employing the dissipative Gross-Pitaevskii equation. The study focused on characterizing quasistationary states under varying forcing, damping, and healing-length parameters. A primary observation involved the mutual-friction acceleration, which demonstrated a cubic scaling relationship with the mean relative velocity between the superfluid and normal-fluid components. The coefficient governing this cubic scaling was found to be associated with a phenomenological damping parameter. Additionally, the intervortex spacing exhibited a dimensional scaling consistent with expectations in a weak-forcing regime. Comparison of findings with a straight-vortex-line model suggested an approximately isotropic distribution of vortex-line orientations.
Approach
The research employed numerical simulations of the dissipative Gross-Pitaevskii equation. This equation models the behavior of the superfluid component in thermal-counterflow turbulence. The simulations were configured to establish quasistationary states, which were achieved across a range of input parameters. These parameters included forcing strength, damping coefficients, and the healing length of the superfluid. The investigation involved analyzing the resulting mutual-friction acceleration and intervortex spacing within these simulated turbulent states. A straight-vortex-line model was utilized as a comparative framework to infer properties of vortex-line orientation.
Findings
- Quasistationary states were attained in the bulk region of thermal-counterflow turbulence across variations in forcing, damping, and healing-length parameters.
- The mutual-friction acceleration exhibited a cubic scaling with the mean relative velocity between the superfluid and normal-fluid components. This relationship can be expressed as $a_{mf} \propto (v_{rel})^3$, where $a_{mf}$ is mutual-friction acceleration and $v_{rel}$ is the mean relative velocity.
- The coefficient that governs this cubic scaling in mutual-friction acceleration was found to be linked to the phenomenological damping parameter integrated into the simulation model.
- Intervortex spacing was observed to follow the expected dimensional scaling when the system operated in a weak-forcing regime.
- A comparison of the simulation results with a straight-vortex-line model indicated that the orientations of the vortex lines were nearly isotropic.