Toward a dynamo model for the solar tachocline

The generation of magnetic field on the Sun is caused by a dynamo mechanism, and is related with the differential rotation of the solar interior. Helioseismologic observations show that strong velocity gradients concentrate in a thin layer located at the base of the convective region, known as the tachocline. This remarkable observational finding lends support to a theoretical model for the solar dynamo, based on a magnetohydrodynamic extension of the so called shallow water approximation. We developed a numerical code to integrate the dynamic equations. Our analysis shows an initial stage during which the magnetic energy grows exponentially fast. In a subsequent stage we find that magnetic energy keeps growing until it reaches equipartition with the mechanical energy of the flow.