  The solar tachocline is a shear layer located at the base of the solar
convection zone. The horizontal shear in the tachocline is likely turbulent,
and it is often assumed that this turbulence would be strongly anisotropic as a
result of the local stratification. What role this turbulence plays in the
tachocline dynamics, however, remains to be determined. In particular, it is
not clear whether it would result in a turbulent eddy diffusivity, or
anti-diffusivity, or something else entirely. In this paper, we present the
first direct numerical simulations of turbulence in horizontal shear flows at
low Prandtl number, in an idealized model that ignores rotation and magnetic
fields. We find that several regimes exist, depending on the relative
importance of the stratification, viscosity and thermal diffusivity. Our
results suggest that the tachocline is in the stratified turbulence regime,
which has very specific properties controlled by a balance between buoyancy,
inertia, and thermal diffusion.
