Enhanced phase mixing of torsional Alfven waves in stratified and divergent solar coronal structures - II. Non-linear simulations

We use magnetohydrodynamic (MHD) simulations to detect the non-linear effects of torsional Alfven wave propagation in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. In Paper I, we considered solutions to the linearized governing equations for torsional Alfven wave propagation and showed, using a finite difference solver we developed named WiggleWave, that in certain scenarios wave damping is stronger than what would be predicted by our analytical solutions. In this paper, we consider whether damping would be further enhanced by the presence of non-linear effects. We begin by deriving the non-linear governing equations for torsional Alfven wave propagation and identifying the terms that cause coupling to magnetosonic perturbations. We then compare simulation outputs from an MHD solver called Lare3d, which solves the full set of non-linear MHD equations, to the outputs from WiggleWave to detect non-linear effects such as: the excitation of magnetosonic waves by the Alfven wave, self-interaction of the Alfven wave through coupling to the induced magnetosonic waves, and the formation of shock waves higher in the atmosphere caused by the steepening of these compressive perturbations. We suggest that the presence of these non-linear effects in the solar corona would lead to Alfven wave heating that exceeds the expectation from the phase mixing alone.