A search for Chandler and nearly diurnal free wobbles using Liouville equations

The basic equations describing the dynamical effects of the Earth's fluid core (Liouville, Navier-Stokes and elasticity equations) are derived for an ellipsoidal earth model without axial symmetry but with an homogeneous and deformable fluid core and elastic mantle. We develop the balance of moment of momentum up to the second order and use Love numbers to describe the inertia tensor's variations. The inertial torque takes into account the ellipticity and the volume change of the liquid core. On the core—mantle boundary we locate dissipative, magnetic and viscous torques. In this way we obtain quite a complete formulation for the Liouville equations. These equations are restricted in order to obtain the usual Chandler and nearly diurnal eigenfrequencies. Then we propose a method for calculating the perturbations of these eigenfrequencies when considering additional terms in the Liouville equations.