Understanding the existence and the dynamics of the magnetic field of the Earth, of the Sun and, in general, of other celestial bodies (dynamo effect) remains one of the most challenging problems of classical physics. Analytical approaches of this problem are extremely complicated while numerical efforts are limited to a range of parameter space that is often quite distant from the realistic systems. For instance, in certain astrophysical bodies as well as in laboratory experiments, the kinematic viscosity v of the fluid is six orders of magnitude smaller than its resistivity η. The two dissipation processes therefore take place at very different time scales. This property makes direct numerical simulations of dynamo intractable. Due to these reasons, we resort to simplified models.
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