  The three-dimensional, hydrodynamic stability of the solar tachocline is
investigated based on a rotation profile as a function of both latitude and
radius. By varying the amplitude of the latitudinal differential rotation, we
find linear stability limits at various Reynolds numbers by numerical
computations. We repeated the computations with different latitudinal and
radial dependences of the angular velocity. The stability limits are all higher
than those previously found from two-dimensional approximations and higher than
the shear expected in the Sun. It is concluded that any part of the tachocline
which is radiative is hydrodynamically stable against small perturbations.
