Mean-Field Magnetohydrodynamics Models as Scaling Limits of Stochastic Induction Equations

Abstract: We study the asymptotic properties of a stochastic model for the induction equations of the magnetic field in a three dimensional periodic domain. The turbulent velocity field driving the electromotive force on the magnetic field is modeled by a noise white in time. For this model we rigorously take a scaling limit leading to a deterministic model. While in case of isotropic turbulence this produces an additional dissipation in the limit model which influences also the decay rate of the Magnetic field in the stochastic model, the case of turbulence devoloped in a preferential direction allows us to find a dynamo effect.