Inertial modes in the liquid core of the Earth

Abstract

Using the simple model of an incompressible fluid, we have computed the eigenfrequencies of the lowest-order inertial modes (azimuthal wavenumber m = 0,1,2) in a spherical shell with the same aspect ratio as the 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 also studied the effect of a thin stable layer lying just below the core-mantle boundary, with the remainder of the core being neutrally stratified, as suggested by recent work. For plausible Nusselt numbers (0.8–0.9), the frequencies of the large-scale modes are only slightly increased (at best by 10 −4).