Revisit the theory of Earth rotation—anatomy of the Liouville equation

Abstract

SUMMARY By anatomizing the classic Liouville equation (LE), an alternative theoretical framework is established for the Earth polar motion where the turbulent time derivative of the fluid forcing, Lforce, is eliminated. The observed polar motion is found a lumped signal of two physical variables, one of which is the forced polar motion, mforce, that balances out the fluid forcing through a simple algebraic identity. The second component is the inertial polar motion, minert, which conserves the total angular momentum by the restoring power of the equatorial bulge. Aside from its numerical difficulties, the time derivative dLforce/dt has proved to be a redundant artefact that mixes the physical signals in the solution of the LE. By an analytical appraisal, we find that for non-Chandler forced polar motions, the dLforce/dt term in the excitation function of the classic LE is 100 per cent responsible for the forced term, mforce, and contributes 0.3 per cent of the inertial term, minert. The Chandler signal originates exclusively from the inertial polar motion minert. The artefact dLforce/dt perturbs the true Chandler signal from the classic LE by 0.3 per cent. Anatomy of the LE allows us to show that a linearized mechanism for the Chandler Wobble excitation is valid, since the linearized governing equation for the inertial polar motion minert stands as part of the exact solution of the full nonlinear equation. Anatomized polar motion equations are also considered in the presence of ocean tides, under the lunisolar torque, and on an elastically deformable Earth. Inaccuracies and misinterpretations associated with the classic LE under those circumstances are clarified in formulating the anatomized polar motion equation group.