Dynamics of the fast solar tachocline. I. Dipolar field

One possible scenario for the origin of the solar tachocline, known as the ``fast tachocline'', assumes that the turbulent diffusivity exceeds eta >~ 10⁹ cm² s^-1. 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 Pr_m=0.1-10, and the meridional flow amplitude (-3 to +3 cm s^-1), 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 10³-10⁴ G, for all parameter combinations considered here. The thickness of the tachocline shows a marked dependence on both time and latitude. The latitude dependence is similar to that inferred by helioseismology, while the time dependence is within the observational errors.