  One possible scenario for the origin of the solar tachocline, known as the
"fast tachocline", assumes that the turbulent diffusivity exceeds eta>10^9
cm^2/s. In this case the dynamics will be governed by the dynamo-generated
oscillatory magnetic field on relatively short timescales. Here, for the first
time, we present detailed numerical models for the fast solar tachocline with
all components of the magnetic field calculated explicitly, assuming axial
symmetry and a constant turbulent diffusivity eta and viscosity nu. We find
that a sufficiently strong oscillatory poloidal field with dipolar latitude
dependence at the tachocline-convective zone boundary is able to confine the
tachocline. Exploring the three-dimensional parameter space defined by the
viscosity in the range log(nu)=9-11, the magnetic Prandtl number in the range
Prm=0.1-10, and the meridional flow amplitude (-3 to +3 cm/s), we also find
that the confining field strength B_conf, necessary to reproduce the observed
thickness of the tachocline, increases with viscosity nu, with magnetic Prandtl
number nu/eta, and with equatorward meridional flow speed. Nevertheless, the
resulting B_conf values remain quite reasonable, in the range 10^3-10^4 G, for
all parameter combinations considered here. The thickness of the tachocline
shows a marked dependence on both time and latitude. A comparison with seismic
constraints suggests that best agreement with our models is achieved for the
highest values of nu and Prm considered here.
