On the coupling between magnetic field and nutation in a numerical integration approach

Nutation amplitudes are computed in a displacement field approach that incorporates the influence of a prescribed magnetic field inside the Earth's core. The existence of relative nutational motions between the liquid core and its surrounding solid parts induces a shearing of the magnetic field. An incremental magnetic field is then created, which in return perturbs the nutations themselves. This problem has already been addressed within a nutation model computed from an angular momentum budget approach. Here we incorporate the magnetic field influence directly in the motion equation and in the boundary conditions used in precise nutation theory, and a new strategy to compute nutations is established. As in previous studies, we assume that the root‐mean‐square of the radial magnetic field amplitude at the core‐mantle boundary is 6.9 Gauss, that the magnetic diffusivity at the bottom of the mantle and in the fluid outer core side is 1.6 m 2 /s, and that the thickness of the conductive layer at the bottom of the mantle is 200 m. The Coriolis force is included in this work. The results show that the free core nutation period decreases by 0.38 days, and that the out‐of‐phase (in‐phase) amplitudes of the retrograde 18.6 year and the retrograde annual nutations increase (decrease) by 20 and 39 μas , respectively. Comparisons of these results with previous studies are made, and discussions are also presented on the contribution of Coriolis force and the prescribed magnetic field on the coupling constants.