  To understand the fundamental physical processes important for the evolution
of solar rotation and distribution of chemical species, we provide theoretical
predictions for particle mixing and momentum transport in the stably stratified
tachocline. By envisioning that turbulence is driven externally in the
tachocline (e.g. by plume penetration), we compute the amplitude of turbulent
flow, turbulent particle diffusivities, and eddy viscosity, by incorporating
the effect of a strong radial differential rotation and stable stratification.
We identify the different roles that the shear flow and stable stratification
play in turbulence regulation and transport. Particle transport is found to be
severely quenched due to stable stratification as well as radial differential
rotation, especially in the radial direction with an effectively more efficient
horizontal transport. The eddy viscosity is shown to become negative for
parameter values typical of the tachocline, suggesting that turbulence in the
stably stratified tachocline leads to a non-uniform radial differential
rotation. Similar results also hold in the radiative interiors of stars, in
general.
