Forced MHD Turbulence Simulations for Coronal Loop Heating

In this work we revisit the question of whether the assumption of a turbulent photosphere provides an efficient mechanism for the disposition of energy in the solar corona. Through a two-dimensional incompressible MHD spectral code and appropriate analysis we investigate the long time statistical behavior of a two-dimensional cross section of a coronal loop. In particular we study the transition to turbulence from a large scale quasi-stationary coherent forcing analyzing the effects of the finite Reynolds and Lundquist numbers and the role of noise in triggering resistive instabilities and subsequent cascades. Simulations of the average energy dissipation and the spectral and spatial distribution at a given time show the self-organization of the loop at large scales via an inverse MHD cascade. To quantify the nonlinearity of the response in the case of constant time forcing, we derive scaling laws against resistivity of the difference between the numerical solution and the linear approximation as well as of the time it takes the system to reach the peak after exceeding the linear approximation solution. We finally comment on the response of the loop also on the most general case of time dependent random forcing comparing with the first case.