Large scale instabilities in two-dimensional magnetohydrodynamics

The stability of a sheared magnetic field is analyzed in two-dimensional ma gnetohydrodynamics with resistive and viscous dissipation. Using a multiple -scale analysis, it is shown that at large enough Reynolds numbers the basi c state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the cr itical point where the instability sets in, in this marginally unstable cas e the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a fina l new equilibrium state. High resolution numerical simulations confirm quan titatively the predictions of multiscale analysis.