I will present numerical models for the geodynamo and argue that despite the very moderate values used in numerical models (which could suggest that all terms are on equal footing), numerical models do exhibit well identified forces balance. Indeed existing numerical models of the geodynamo are usually classified in two categories: dipolar modes, when the inertial term is small enough, and multipolar fluctuating dynamos, for stronger forcing.
I show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong field limit. This solution co-exists with the often described viscous branch.
Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length-scale, and the strong field branch in which visous and inertial effects are largely negligeable.
I argue that in most available models today, the intrinsic quadratic non-linearities in the Navier-Stokes equation are over-estimated and blur the classical picture of the Weak and Strong field branches.
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