Nonlinear turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a two-dimensional magnetohydrodynamic turbulence

TL;DR

This paper investigates how nonlinear effects influence the suppression of turbulent magnetic diffusion and drift velocity in two-dimensional MHD turbulence, revealing conditions where catastrophic quenching is avoided at high magnetic Reynolds numbers.

Contribution

It demonstrates that the quenching of turbulent magnetic diffusion is mitigated when the flux divergence of mean-square magnetic potential is non-zero, challenging previous notions of universal catastrophic quenching.

Findings

Catastrophic quenching does not occur for large-scale magnetic fields when flux divergence is non-zero.

Quenching becomes independent of magnetic Reynolds number under certain flux conditions.

Analogous behavior to 3D MHD turbulence regarding magnetic helicity flux and alpha effect.

Abstract

We study a nonlinear quenching of turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a developed two-dimensional MHD turbulence at large magnetic Reynolds numbers. We show that transport of the mean-square magnetic potential strongly changes quenching of turbulent magnetic diffusion. In particularly, the catastrophic quenching of turbulent magnetic diffusion does not occur for the large-scale magnetic fields $B \gg B_{\rm eq} / \sqrt{\rm Rm}$ when a divergence of the flux of the mean-square magnetic potential is not zero, where $B_{\rm eq}$ is the equipartition mean magnetic field determined by the turbulent kinetic energy and Rm is the magnetic Reynolds number. In this case the quenching of turbulent magnetic diffusion is independent of magnetic Reynolds number. The situation is similar to three-dimensional MHD turbulence at large magnetic Reynolds numbers whereby the catastrophic quenching of the alpha effect does not occur when a divergence of the flux of the small-scale magnetic helicity is not zero.