Numerical Study of Velocity Statistics in Steady Counterflow Quantum Turbulence

TL;DR

This study analyzes velocity statistics in steady counterflow quantum turbulence, revealing Gaussian and power-law behaviors in velocity PDFs and the effects of anisotropy on velocity distributions.

Contribution

It provides a detailed numerical analysis of velocity PDFs in quantum turbulence, highlighting the transition point and anisotropic effects.

Findings

Velocity PDF is Gaussian at low velocities.

High-velocity tail follows a $v^{-3}$ power law.

Anisotropy affects velocity distributions parallel and perpendicular to counterflow.

Abstract

We investigate the velocity statistics by calculating the Biot--Savart velocity induced by vortex filaments in steady counterflow turbulence investigated in a previous study [Phys. Rev. B {\bf 81}, 104511 (2010)]. The probability density function (PDF) obeys a Gaussian distribution in the low-velocity region and a power-law distribution $v^{-3}$ in the high-velocity region. This transition between the two distributions occur at the velocity characterized by the mean inter-vortex distance. Counterflow turbulence causes anisotropy of the vortex tangle, which leads to a difference in the PDF for the velocities perpendicular to and parallel to the counterflow.