On limiting the thickness of the solar tachocline

We present axisymmetric simulations of the coupled convective and radiative regions in the Sun in order to investigate the angular momentum evolution of the radiative interior. Both hydrodynamic and magnetohydrodynamic models were run. We find an initial rapid adjustment in which the differential rotation of the convection zone viscously spreads into the radiative interior, thus forming a "tachocline." In polar regions, the subsequent spread of the tachocline is halted by a counterrotating meridional circulation cell which develops in the tachocline. Near the equator such a counterrotating cell is more intermittent and the tachocline penetration depth continues to increase, albeit more slowly than previously predicted. In the magnetic models, we impose a dipolar field initially confined to the radiative interior. The behavior of the magnetic models is very similar to their non-magnetic counterparts. Despite being connected to the convection zone, very little angular momentum is transferred between the convective and radiative regions. Therefore, while it appears that a magnetic field is not necessary to stop the tachocline spread, it also does not promote such a spread if connected to the convection zone.