A Renormalisation Group Analysis of 2d Freely Decaying Magnetohydrodynamic Turbulence

TL;DR

This paper applies renormalisation group theory to analyze the long-term behavior of two-dimensional freely decaying magnetohydrodynamic turbulence, revealing connections to non-unitary conformal field theories and energy spectrum relations.

Contribution

It introduces a novel RG framework for MHD turbulence, linking probability laws to conformal field theories and constructing fixed points from minimal models.

Findings

Kinetic and magnetic energy spectra are proportional in the long-time regime.

Probability laws evolve via renormalisation transformations.

Constructed fixed points using non-unitary minimal models.

Abstract

We study two dimensional freely decaying magnetohydrodynamic turbulence. We investigate the time evolution of the probability law of the gauge field and the stream function. Assuming that this probability law is initially defined by a statistical field theory in the basin of attraction of a renormalisation group fixed point, we show that its time evolution is generated by renormalisation transformations. In the long time regime, the probability law is described by non-unitary conformal field theories. In that case, we prove that the kinetic and magnetic energy spectra are proportional. We then construct a family of fixed points using the $(p,p+2)$ non-unitary minimal models of conformal field theories.