Conformal Models of Magnetohydrodynamic Turbulence

TL;DR

This paper explores conformal models of 2D magnetohydrodynamic turbulence, revealing conditions for solutions and extending analysis to finite conductivity, thus advancing theoretical understanding of MHD turbulence.

Contribution

It demonstrates the existence of non-unitary minimal model solutions in 2D MHD derived from 3D, and extends the analysis to finite conductivity cases with approximate solutions.

Findings

Solutions exist under perpendicular flow conditions.

Finite conductivity solutions are approximated and related to ideal cases.

Conditions for conformal turbulence models are clarified.

Abstract

Following the previous work of Ferretti and Yang on the role of magnetic fields in the theory of conformal turbulence, we show that non-unitary minimal model solutions to 2-dimensional magnetohydrodynamics (MHD) obtained by dimensional reduction from 3-dimensions exist under different (and more restrictive) conditions. From a 3-dimensional point of view, these conditions are equivalent to perpendicular flow, in which the magnetic and velocity fields are orthogonal. We also extend the analysis to the finite conductivity case and present some approximate solutions, whose connection to the exact ones of the infinite conductivity case is also discussed.