Analytical computation of total topographic torque at the core-mantle boundary and its impact on tidally driven length-of-day variations

The Earth's rotation exhibits periodic variations as a result of gravitational torques exerted by the Sun and the Moon and of angular momentum exchange of the solid Earth with the Earth's atmosphere and hydrosphere. Here, we aim at determining the complementary effect of the deep interior on variations in the length-of-day (LOD) and focus on the influence of topography at the core-mantle boundary (CMB). For this purpose, we have developed an analytical approach for solving the Navier-Stokes equation for global rotational motions and inertial waves, based on and extending the approach of Wu & Wahr (). An advantage of the analytical approach is that it allows to identify the frequencies and topographic spherical harmonics degrees and orders where resonance can happen, as well as to quantify the total amplifications in the tidal effects on LOD variations. Although the resonances are found to be sometimes quite near tidal frequencies, we show that they are not sufficiently close to induce significant perturbations in LOD variations, except for two of the tides, the fortnightly and monthly tides M-f and M-m. Our results go beyond the findings of Wu & Wahr (), extending them to a much wider range of degrees and orders of topographic coefficients. We show that there is an amplification in M-f and M-m induced by the degree 18-order 10 and by the degree 7-order 1 of the topography, respectively. Our approach is generic in the sense that it can be applied to other orientation changes of the Earth as well as to other planets.