Magnetic confinement of the solar tachocline: II. Coupling to a   convection zone
  The reason for the observed thinness of the solar tachocline is still not well understood. One of the explanations that have been proposed is that a primordial magnetic field renders the rotation uniform in the radiation zone. We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone. The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computational domain extends from $0.07\;R_\odot$ to $0.97\;R_\odot$. In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis can not remain confined in the radiation zone. When the field lines are allowed to interact with turbulent unstationary convective motions at the base of the convection zone, 3D effects prevent the field confinement. In agreement with previous work, we find that a dipolar fossil field, even when it is initially buried deep inside the radiation zone, will spread into the convective zone. According to Ferraro's law of iso-rotation, it then imprints on the radiation zone the latitudinal differential rotation of the convection zone, which is not observed. 
A. Strugarek, A. S. Brun and J.-P. Zahn
astro-ph.SR