A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.

The parametric instability of two-dimensional Alfvénic turbulence has been studied via direct numerical simulations of magnetohydrodynamics. A general form for an Alfvénic fluctuation is derived, with a strongly anisotropic spectrum with respect to a mean magnetic field, typical of the solar wind. Perturbing this solution, an exponential growth of both compressive and backward-propagating Alfvénic fluctuations has been observed. At variance with previous 1D studies, it has been observed that the growth rate tends to increase with the plasma β. Unstable modes manifest as strongly localized, coherent, field-aligned, stream-like structures, with anticorrelation between magnetic and density fluctuations, in agreement with observations. These results might help us to understand the development of turbulence in the solar wind as well as in stellar winds.

Large-scale dynamo action is well understood when the magnetic Reynolds number (Rm) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias & Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work to the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias & Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average.

High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD). The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.