Abstract

Astrophysical fluids are conductive, magnetized and turbulent. This entails a variety of phenomena, two most basic of which is the dynamo and the energy cascade. Very well known empirically in hydrodynamics, so called “zeroth law of turbulence”, states that even if viscosity goes to zero, energy dissipation does not, but goes to a constant. It turns out that in MHD not only this still holds true, but another basic law, which I call “zeroth law of dynamo”, is valid, namely that if Reynolds numbers are sufficiently high and magnetic energy is low, the latter will grow at a constant rate, which is a fraction of the total dissipation rate. Another point of interest for an astrophysicist is the properties of MHD cascade in the inertial range. I will argue that both theory and numerics favor Kolmogorov -5/3 slope and not -3/2 slope that was reported earlier. The most challenging problem is so-called imbalanced, or cross-helical case which appear whenever there is a localized source of perturbations, such as the Sun for the solar wind turbulence or the central engine in AGN jets. The standard Goldreich-Sridhar model does not apply in this case and it eluded theoretical description for a long time. The keys to understand energy cascades in the imbalanced case are the anisotropies of the Elsasser fields which turn out to be different. I will show the results of one of the highest resolution simulations ever performed, which were very helpful in discriminating between various viable models of MHD turbulence.