Wobble/nutation of a rotating ellipsoidal Earth with liquid outer core: implementation of a new set of equations describing dynamics of rotating fluids

Abstract

In this thesis I implement a new set of scalar equations describing the free oscillations of rotating self-gravitating compressible fluids, to solve for the wobble and inertial modes of a rotating Earth with rigid mantle and liquid core. A Galerkin method is used to integrate these equations in the liquid core. It is shown that by using the divergence theorem it is possible to make use of the 'natural' boundary conditions to reduce the order of the derivatives from second to first in the Galerkin formulation of the governing equations. As a partial test of the reliability of our formulation, the eigenperiods of the Earth's Chandler wobble (CW), nearly diurnal free wobble (NDFW) and some of the other inertial modes are computed for the case of a compressible, but neutrally stratified, core and compared to those for the homogeneous incompressible core model.