Effect of rotation on the tachoclinic transport

Aims. We study the effect of rotation on sheared turbulence, due to differential rotation in the solar tachocline. Methods. By solving quasi-linear equations for the fluctuating fields, we derive turbulence amplitude and turbulent transport coefficients (turbulent viscosity and diffusivity), taking into account the effects of shear and rotation on turbulence. We focus on the tachocline regions near the equator and the poles where the rotation and the shear are perpendicular and parallel, respectively. Results. For parameters values typical of the tachocline, we show that the shear reduces both turbulence amplitude and transport, more strongly in the radial direction (parallel to the shear) than in the horizontal one, resulting in an anisotropic turbulence. The rotation further reduces turbulence amplitude and transport at the equator whereas it does not have much effect near the pole. The interaction between the shear and the rotation is shown to give rise to a novel non diffusive flux of angular momentum (known as the Λ effect), possibly offering a mechanism for the occurrence of a strong shear region in the solar interior. Further implications for the transport in the tachocline are discussed.