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 diusivity exceeds > 10 9 cm 2 s 1 . In this case the dynamics will be governed by the dynamo- generated oscillatory magnetic eld on relatively short timescales. Here, for the rst time, we present detailed numerical models for the fast solar tachocline with all components of the magnetic eld calculated explicitly, assuming axial symmetry and a constant turbulent diusivity and viscosity . We nd that a suciently strong oscillatory poloidal eld with dipolar latitude dependence at the tachocline{convective zone boundary is able to conne the tachocline. Exploring the three-dimensional parameter space dened by the viscosity in the range log = 9{11, the magnetic Prandtl number in the range Prm =0 :1 10, and the meridional flow amplitude ( 3t o +3 cm s 1 ), we also nd that the conning eld strength Bconf, necessary to reproduce the observed thickness of the tachocline, increases with viscosity , with magnetic Prandtl number =, and with equatorward meridional flow speed. Nevertheless, the resulting Bconf 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. The latitude dependence is similar to that inferred by helioseismology, while the time dependence is within the observational errors.