Scaling properties in MHD turbulence

The article first gives a brief review of the main properties of MHD turbulence, which are governed by the selective decay of the ideal invariants and the Alfvén effect. The inertial range behaviour is reflected in the geometric properties of level surfaces. These are predicted to have fractal dimension , which is verified in numerical simulations. The second part deals with the statistical properties. Probability density functions of the velocity and magnetic field increments and the energy dissipation rate are discussed. The simulations are complemented by the analysis of a simple shell model for MHD turbulence, taking into account the Alfvén effect. It is found that the latter is more subtle than anticipated