Mechanism of the interannual oscillation in length of day and its constraint on the electromagnetic coupling at the core-mantle boundary

A significant 6 yr oscillation exists in the length of day (LOD) on the interannual scales. There are mainly two models currently to explain this oscillation, i.e., mantle-inner core gravitational (MICG) coupling mode and the fast torsional waves within the fluid outer core. The former has been doubted, while the source of the excitation of the latter is not yet understood. Therefore, the mechanism of the 6 yr oscillation is still not clear. Here, by considering the mantle and inner core angular momentum, we investigate the MICG coupling mode and its natural period (T0). Given that the strength of gravitational core-mantle coupling (Γ¯) within a recently constrained range is quite weaker than that estimated previously, the mechanism of the 6 yr oscillation still can be attributed to MICG coupling mode (i.e., T0 equals to 6 yrs), but, we require the inertia moment of fluid within the tangent cylinder involved in the 6 yr oscillation to be smaller than 1.23×1035kgm2. This interpretation can be used to constrain the electromagnetic (EM) coupling at the inner core boundary (ICB). In order to study quantitatively the constraints on the EM coupling at the core-mantle boundary (CMB) from the observed 6 yr oscillation with a quality factor Q (∼51.6), we further develop the mathematical expression between the Q value based on the observations and EM coupling at the CMB. According to the Γ¯ value from recent estimates and assuming that the 6 yr oscillation is in a free decay, we can obtain the radial magnetic field at the CMB is 0.52 mT∼0.62 mT when conductance at the CMB is 108 S.