Using the simple model of an incompressible fluid, we have computed th
e eigenfrequencies of the lowest-order inertial modes (azimuthal waven
umber m = 0,1,2) in a spherical shell with the same aspect ratio as th
e liquid core of the Earth. The computed eigenfunctions show that all
inertial modes have strong oscillating shear layers. For the very low
Ekman number appropriate to the core, these layers might be the origin
of some small-scale turbulence through shear instabilities. We have a
lso studied the effect of a thin stable layer lying just below the cor
e-mantle boundary, with the remainder of the core being neutrally stra
tified, as suggested by recent work. For plausible Nusselt numbers (0.
8-0.9), the frequencies of the large-scale modes are only slightly inc
reased (at best by 10(-4)).