  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.
