Numerical Studies of Counterflow Turbulence, Velocity Distribution of Vortices

TL;DR

This paper presents advanced numerical simulations of quantum turbulence in superfluid helium, overcoming previous limitations to accurately reproduce steady-state vortex behavior and match experimental observations.

Contribution

We developed a simulation method that avoids the unphysical assumptions of earlier models, accurately capturing steady-state turbulence in superfluid helium.

Findings

Established the relation L=γ² v_ns² with quantitative agreement for γ

Achieved steady-state turbulence without the localized induction approximation

Compared numerical results successfully with experimental visualizations

Abstract

We performed the numerical simulation of quantum turbulence produced by thermal counterflow in superfluid $^{4}${\rm He} by using the vortex filament model. The pioneering work was made by Schwarz, which has two defects. One is neglecting non-local terms of the Biot-Savart integral (localized induction approximation, LIA), and the other is the unphysical mixing procedure in order to sustain the statistically steady state of turbulence. We succeeded in making the statistically steady state without the LIA and the mixing. This state shows the characteristic relation $L=\gamma^2 v_{ns}^2$ between the line-length-density $L$ and the counterflow relative velocity $v_{ns}$ with the quantitative agreement of the coefficient $\gamma$ with some typical observations. We compare our numerical results to the observation of experiment by Paoletti {\it et al}, where thermal couterflow was visualized by solid hydrogen particles.