Density Stratification in Rotating Spherical Fluid Shells: Application to the Earth’s Fluid Core

Abstract:

The Earth’s outer core is a rotating ellipsoidal shell of compressible, stratified and self-gravitating fluid. The Galerkin method is applied to study the effects of density stratification on the frequencies of the inertial modes for a compressible shell proportional to the realistic Earth’s fluid core. The inertial modes of the core are the free oscillations with periods longer than half of a day and have the Coriolis force as their restoring force. Historically an incompressible and homogeneous fluid sphere is considered to study these modes and analytical solutions are known for the frequencies and the displacement eigenfunctions of this model. The three potential description (3PD) is used to a compressible and stratified fluid core model with different stratification parameters β, related to the local Brunt-Väisälä frequency. As a first approximation, however, we ignore the ellipticity of the core’s figure. The 3PD scheme describes the exact linearized dynamics of rotating, self-gravitating, stratified, compressible and inviscid fluids. We show that, depending on the size of β, some modal frequencies and eigenfunctions are practically unaffected by stratification, some are changed and some modes may disappear. We also first derive the web of characteristics, which gives more information about the eigenfunctions of these modes, as functions of frequency and stratification for compressible and inviscid fluids.