Some remarks about the rotations of a viscous planet and its homogeneous liquid core: linear theory

Linear equations governing the rotation of the Earth are developed for a model with a Maxwell homogeneous mantle and a homogeneous inviscid fluid core having a differential rotation relative to the mantle. We find four eigenfrequencies for the equatorial perturbations in rotation. Two are well known: the rotational nearly diurnal frequency and the Chandlerian frequency with a damping related to the relaxation time of the Earth. The other two frequencies, one being a heavily damped long-period oscillation and the other one zero, are related to the relaxation modes, but are nevertheless coupled with the rotational eigenfrequencies. We investigate the kinetic and deformation energy resulting from both impulsive and time-constant geophysical sources. Using a generalized notation, we derive an analytical solution for the rotations of the Earth and its fluid core due to various excitation sources at the Earth's surface and at the core-mantle boundary. We obtain some results concerning phenomena acting at the CMB which are able to produce a significant shift of the rotation axis.