Free Oscillations and Forced Movements of Gravitating Viscous Earth Core under Lunar and Solar Attraction

Equations are derived for the motion of a core of arbitrary shape in the viscous incompressible liquid at large Reynolds numbers. Natural oscillations of the solid spherical core in the liquid viscous core are investigated for cases of immovable and rotating shells. Corrections to frequencies of natural oscillations of the solid core are obtained which are caused by the gravitational influence of Earth's imperfections. Analytical formulas are derived for frequencies and a constant displacement of the solid core due to external actions. Contribution of attraction of imperfections at the coremantle boundary, imperfections of Earth’s tectonic shell into the mentioned effects is estimated. Approximated equations of forced movements of the solid core inside a rotating cavity are derived; their approximated solution is constructed, and disturbances in the motion of Earth’s solid core under the lunar and solar attraction are estimated.