Helioseismic inversions of the Sun's internal angular velocity profile show
that the rotation changes from differential in latitude in the convection
zone to almost uniform in the radiative region below. The transition occurs
in a thin layer, the tachocline, which is the seat of strong shear in the
vertical direction. In this Note we examine whether this rotation profile c
an lead to shear turbulence at the top of the radiation zone. By using the
standard solar model, we show that such turbulence can be generated only in
a narrow region 0.695 R. less than or similar to r < 0.713 R. at the equat
or and even in narrower layers at higher latitudes. We conclude that the tu
rbulence generated by this vertical shear is unlikely to play a significant
role in the transport of matter and angular momentum, and that other mecha
nisms must be invoked to achieve this.