On a long-term dynamics of the magnetised solar tachocline

Aims. We investigate the confinement and long-term dynamics of the magnetised solar tachocline. Methods. Starting from first principles, we derive the values of turbulent transport coefficients in the magnetised solar tachocline and then explore the implications for the confinement and long-term dynamics of the tachocline. Results. For reasonable parameter values, the turbulent eddy viscosity is found to be negative, with turbulence enhancing the radial shear in the tachocline. Both magnetic diffusivity and thermal diffusivity are severely quenched, with the values much smaller than the magnitude of the eddy viscosity. The effect of the meridional circulation on momentum transport via the hyperviscosity becomes important when the radial shear becomes large (larger than the presently inferred value) due to the negative viscosity. The results imply that the tachocline develops too strong radial shear to be a stationary Hartmann layer. In the limit of a strong radiative damping where the turbulence is active on very small scales (< 10R⊙), the eddy viscosity can become positive although its effect is likely to be dominated by the hyperviscosity. In comparison with the momentum transport, the transport of magnetic field, heat, and passive particles is more severely quenched. The results imply that the tachocline of thickness is larger than O(10R⊙), independent of the strength of magnetic fields. In addition, the momentum transport is much more efficient than the particle mixing in the tachocline, consistent with the observations.