INERTIAL MODES IN THE LIQUID-CORE OF THE EARTH

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)).