Gravitational interactions of the solid core and the Earth’s mantle and variations in the length of the day

Abstract

A simple mechanical model explaining the long-period (about 100-year) variations in the Earth’s rotational velocity is proposed. This model takes into account the gravitational interaction of the mantle with the solid core of the Earth and the fact that the core rotation leads that of the mantle. Well-known Earth parameters provide estimates of the gravitational torque that support the proposed model. The mathematical problem involved reduces to the classical problem of a nonlinear oscillator exposed to a constant torque. The well-known parameters of the core-mantle system result in a stable equilibrium and a stable limiting cycle on the phase cylinder of this oscillator. This equilibrium corresponds to a single angular velocity for the mantle and solid core, with no long-period oscillations in the length of the day. The limiting cycle corresponds to the core rotation leading the mantle rotation. In this case, the ellipsoidality of the gravitationally interacting bodies provides a periodic interchange of kinetic angular momentum between the mantle and solid core that results in long-period variations in the length of the day. The proposed model does not support the formerly widespread opinion that the core rotates more slowly than the mantle.