Analytical computation of the effects of the core-mantle boundary topography on tidal length-of-day variations

We have computed coupling mechanisms at the core-mantle boundaries of terrestrial bodies of the Solar system, and in particular, the pressure torque on the topography at the core-mantle boundary. The philosophy of the computation follows Wu and Wahr (1997), which allows to solve for the velocity field coefficients in terms of the topography coefficients. The velocity in the fluid core is decomposed into a global classical velocity and an incremental velocity related to the topography. We have used an analytical approach to compute this last part as well as the incremental changes in the periodic variations of the length-of-day (LOD) and in the librations, i.e. oscillating motions in space. We have found that there are topography coefficients that are enhanced due to resonances at particular frequencies. For the Earth the tidal forcing frequencies are compared to those resonance frequencies. The total torque on the core-mantle boundary is demonstrated to be dependent on particular amplitudes of the topography. 1. MOTIVATION The length-of-day variations are usually computed from angular momentum equations of the whole Earth and of the different layers (inner core, outer core and mantle). Coupling mechanisms must be considered at the CMB and ICB (Inner Core Boundary). The torque considered in the classical approach is the gravitational and pressure torques related to the flattening of the core. In a more sophisticated approach and for the nutations, one considered the electromagnetic torque (e.g. Mathews et al., 1991) or even the viscous torque (e.g. Mathews and Guo, 2005). The topographic torque related to the non-hydrostatic part of the CMB shape is not considered, while the problem has been addressed by Wu and Wahr (1997) in a numerical approach. These Figure 1: Results concerning nutations, from Wu and Wahr, 1997 authors have shown that the topographic torque, often disregarded, may be important at CMB. Wu and Wahr (1997) have computed numerically the topographic torque using topography expanded in Spherical Harmonics and have shown that some harmonics of the topography have