Nonlinear magnetohydrodynamic dynamo

Abstract

The self‐consistent nonlinear evolution and saturation of the dynamo, including the back reaction of the magnetic field on the flow through the Lorentz J×B force, is investigated via simulation of the fully compressible magnetohydrodynamic (MHD) equations. The saturated state is found to be highly turbulent. The energy in the saturated magnetic field is only a small fraction of the kinetic energy in the flow which drives the dynamo. However, as the collision frequency decreases and the Reynolds number R increases, the ratio of magnetic to kinetic energy in the saturated state increases gradually. The nonlinear viscosity generated by the turbulent fluctuations rises rapidly relative to the collisional viscosity as R increases, such that the total transport of momentum remains virtually unchanged as the collisional viscosity is reduced. The scale lengths of the magnetic and velocity fluctuations both decrease as R increases, so that the scale size of the magnetic field remains comparable to the scale size of the flow.