Weak turbulence in two-dimensional magnetohydrodynamics

TL;DR

This paper develops a weak turbulence theory for 2D magnetohydrodynamics, analyzing wave interactions and their unique nonlocal features, and explores the evolution beyond weak turbulence including steady state formation.

Contribution

It introduces a novel weak turbulence framework for 2D MHD, highlighting integrability and nonlocal interactions, and extends analysis beyond weak turbulence regimes.

Findings

Wave-kinetic equation in 2D MHD is integrable.

Wave interactions in 2D are nonlocal unlike in 3D.

Strong derivatives of spectra appear at small parallel wavenumbers.

Abstract

A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics (MHD). We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfv\'en waves. Our analysis is greatly helped by the fortunate fact that in 2D the wave-kinetic equation is integrable. In contrast with the 3D case, in 2D the wave interactions are nonlocal. Another distinct feature is that strong derivatives of spectra tend to appear in the region of small parallel (i.e. along the uniform magnetic field direction) wavenumbers leading to a breakdown of the weak turbulence description in this region. We develop a qualitative theory beyond weak turbulence describing subsequent evolution and formation of a steady state.