Long-range correlations and coherent structures in magnetohydrodynamic equilibria

TL;DR

This paper derives an exact equilibrium theory for 2D magnetohydrodynamics, revealing long-range correlations and coherent structures like eddies and jets, differing from previous local approximations and with implications for solar tachocline studies.

Contribution

It introduces an exact equilibrium framework for 2D MHD that captures long-range correlations and coherent structures, contrasting with prior local variational approaches.

Findings

Long-range correlations between magnetic and velocity fields.

Existence of coherent structures such as eddies and jets.

Differences from previous local variational models.

Abstract

The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged correlations between the magnetic and velocity fields. This is quite different from the results of previous variational treatments, which relied on a local product ansatz for the thermodynamic Gibbs distribution. The equilibria display the same type of coherent structures, such as compact eddies and zonal jets, previously found in pure fluid equilibria. Possible consequences of this for recent simulations of the solar tachocline are discussed.