Dynamics of the fast solar tachocline: II. Migrating field
  We present detailed numerical calculations of the fast solar tachocline based on the assumption that the dynamo field dominates over the dynamics of the tachocline. In the present paper of the series, we focus on three shortfalls of the earlier models. First, instead of the simple oscillating dipole poloidal field we study the more general magnetic field structures reminiscent of the butterfly diagram. The migrating field is prescribed as the observed axisymmetric radial magnetic field Stenflo (1988, 1994). Our results are in good agreement with our analitical estimate and our previous works in Forgacs-Dajka & Petrovay (2001,2002), but the polar "dip" in isorotational surfaces is strongly reduced in this case. On the other hand, a more realistic model should have a magnetic diffusivity decreasing significantly inside the radiative interior, so we also explore the effect of diffusivity and magnetic Prandtl number varying with depth. We found that the downwards decreasing magnetic diffusivity and Prandtl number have no significant effect on the solution, although the temporal variation of the tachocline thickness has decreased. 
E. Forgacs-Dajka