Effect of Rossby and Alfven Waves on the Dynamics of the Tachocline

To understand magnetic diffusion, momentum transport, and mixing in theinterior of the sun, we consider an idealized model of the tachocline, namelymagnetohydrodynamics (MHD) turbulence on a $\beta$ plane subject to a largescale shear (provided by the latitudinal differential rotation). This modelenables us to self-consistently derive the influence of shear, Rossby andAlfv\'{e}n waves on the transport properties of turbulence. In the strongmagnetic field regime, we find that the turbulent viscosity and diffusivity arereduced by magnetic fields only, similarly to the two-dimensional MHD case(without Rossby waves). In the weak magnetic field regime, we find a crossoverscale ($L\_R$) from a Alfv\'{e}n dominated regime (on small scales) to a Rossbydominated regime (on large scales). For parameter values typical of thetachocline, $L\_R$ is larger that the solar radius so that Rossby waves areunlikely to play an important role in the transport of magnetic field andangular momentum. This is mainly due to the enhancement of magneticback-reaction by shearing which efficiently generates small scales, thus strongcurrents