Second order torque on the tidal redistribution and the Earth's rotation

Abstract

This study presents a complete treatment of the second order torques on the Earth due to the action of each of the three parts of the degree 2 potential (V₂₀: zonal; _V21: tesseral; and V₂₂: sectorial) on the deformations produced by the other parts, and the consequent effects on nutation. The work of Mathews et al. (2002, J. Geophys. Res., 107, B4) contained a treatment of the action of the tesseral potential on tidal deformations, taking into account the presence of the fluid core, and also of the contributions from mantle anelasticity and ocean tides to the deformations. We extend that work to include the actions of the zonal and sectorial potentials too. Our computations show that an almost complete cancellation takes place between reciprocal contributions; the largest net effect reaches -35 µas on the in-phase 18.6-yr nutation in longitude. The total effect found on the precession is 0.1 mas/cy in longitude and in obliquity. The cancellations would have been complete but for the fact that (i) the values of the compliances (deformability parameters) are not the same for deformations excited by the three parts of the degree 2 potential even for a nondissipative Earth and (ii) anelasticity and ocean tides make the contributions to the compliances complex (besides being unequal for the three parts) and thus give rise to out-of-phase components in the response to tidal forcing.