Magnetic Fields and Passive Scalars in Polyakov's Conformal Turbulence

TL;DR

This paper explores conformal field theory models of two-dimensional turbulence, focusing on magnetic fields and passive scalars, and predicts energy distribution behaviors that can be tested astrophysically.

Contribution

It identifies specific minimal models within conformal turbulence that account for magnetic and passive scalar dynamics, highlighting differences from previous models.

Findings

Magnetic energy dominates at larger distances, violating equipartition.

Different minimal models arise at high magnetic Reynolds numbers.

Predictions are applicable to astrophysical phenomena.

Abstract

Polyakov has suggested that two dimensional turbulence might be described by a minimal model of conformal field theory. However, there are many minimal models satisfying the same physical inputs as Polyakov's solution (p,q)=(2,21). Dynamical magnetic fields and passive scalars pose different physical requirements. For large magnetic Reynolds number other minimal models arise. The simplest one, (p,q)=(2,13) makes reasonable predictions that may be tested in the astrophysical context. In particular, the equipartition theorem between magnetic and kinetic energies does not hold: the magnetic one dominates at larger distances.