Effects of topographic coupling at core-mantle boundary in rotation and orientation changes of the Earth.

We study coupling mechanisms at the core-mantle boundary (CMB) of the Earth in the frame of nutations and Length-of-Day (LOD) variations. The CMB is usually considered to have a smooth spherical or elliptical shape inducing a Poincaré flow in the nutation case and a global rotation in the LOD case. However, in reality, the CMB is bumpy and there are mountains and valleys representing local height differences of the order of a kilometer. The existence of a topography induces inertial waves that need to be considered in the flow of the core. This is in addition to the Poincaré fluid motion when the nutations are computed and in addition to a relative rotation of the fluid opposite and of the same amplitude as that of the mantle for LOD variations. The additional pressure and the topographic torque depend on the shape of the CMB and can be related to the spherical harmonic coefficients of the CMB topography. We follow the philosophy of the computation of Wu and Wahr [Geophys. J. Int., 128(1), 18-42, 1997] and determine the coefficients of the velocity field in the core at the CMB in terms of the topography coefficients. We used an analytical approach instead of a numerical one. We confirm that some topography coefficients may enhance length-of-day variations and nutations at selected frequencies, and show that these increased rotation variations and nutations are due to resonance effects with inertial waves in the incremental core flow. While they could be at a detectable level for LOD, they are very small for nutations (except for the flattening of the core), enhancing the importance of the electromagnetic coupling at the CMB.