We briefly present recent progress using the ASH code to model in 3-D the solar convection, dynamo and its coupling to the deep radiative interior. We show how the presence of a self-consistent tachocline influences greatly the organization of the magnetic field and modifies the thermal structure of the convection zone leading to realistic profiles of the mean flows as deduced by helioseismology.

The most promising model for explaining the origin of solar magnetism is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. After discussing how this model explains the regular periodic features of the solar cycle, we come to the questions of what causes irregularities of solar cycles and whether we can predict future cycles. Only if the diffusivity within the convection zone is sufficiently high, the polar field at the sunspot minimum is correlated with strength of the next cycle. This is in conformity with the limited available observational data.

Kinematic solar dynamo models (KSDM) that use a solar like differential rotation profile usually fail to reproduce the latitudinal distribution of the toroidal magnetic fields. Usually, it is assumed that it is the larger radial shear present in the solar tachocline at higher latitudes that is the responsible for such results. We here consider variations in the shape and thickness of the tachocline and find that a better distribution of the toroidal fields is obtained when the thickness of the tachocline is $d_1=0.02R_{\odot}$, a smaller value than that conventionally used.