Numerical models of astrophysical dynamos

International audienceThe parameters regime relevant to dynamo action in astrophysical objects is out of reach of present day numerical models because of computational limitations. It is thus necessary to derive scaling laws to extend numerical results to real world dynamos.We show that traditional power based scaling laws for the magnetic field strength are too general, since they mainly traduce the statistical balance between the energy production and dissipation, and are thus satisfied by any dynamo in statistical equilibrium. We introduce a predictive scaling law (i.e. depending on input parameters only) for the magnetic field strength in numerical dynamos, by guiding our reasoning on physical arguments. We thus show that dipolar dynamos operate in a viscous dynamical regime, which is not relevant to astrophysical objects. Finally, we show that the dipolar-multipolar transition occurring in numerical models can be described by a sole non-dimensional parameter corresponding to a three-terms balance