Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents.