Abstract

Understanding the generation of large-scale magnetic fields and flows in MHD turbulence remains one of the most challenging problems in astrophysical fluid dynamics. The well-studied kinematic theory ignores the possibility of small-scale dynamo action, which is prevalent at high magnetic Reynolds number. Here, we thus examine the possibility of large-scale field (and flow) arising from a fully MHD basic state — as may arise from the saturation of a small-scale dynamo. Under this new theory, four mean field tensors now come into play. In certain cases, such as “short-sudden” turbulence, these tensors may be calculated explicitly. More generally, the (nonlinear) mean field theory works well for mildly turbulent flows, but can fail in strongly disordered systems. This leads us to address the more general dynamical systems question of whether a linear response can be detected following a  small (linear) perturbation to a chaotic system.