Topographic Drag at the Core-Mantle Interface

The length of day variations with periods from five to one hundred years are mainly due to core-mantle interactions. Assuming a differential velocity between the core and the mantle, we investigate the pressure coupling on a core-mantle boundary (CMB) interface with topography. Including rotation, buoyancy, and magnetic effects in local models of the CMB, we provide a taxonomy of the waves radiated by the core flow along the topography. We obtain the local stress with a perturbation approach and a semi-analytical spectral model built upon these waves. We incorporate planetary curvature effects by considering a “non-traditional” $\beta$-plane approximation suited for deep fluid layers and long topography wavelengths. We calculate weakly non-linear flows and characterize the wave drag mechanism. Unlike previous works, our analysis is not restricted to strong stratification or short wavelengths. It reveals the significant impact of the Rossby waves on stress. We also show that these waves are drastically modified when considering two-dimensional topographies instead of simple ridges. For a buoyancy frequency $N$ at least comparable to the rotation frequency, the main factors defining the stress are $N$ and $\sqrt{U_0}$ for the small velocity amplitudes $U_0$ relevant for the Earth's core. We document the departures from this scaling law as the velocity is increased. The main part of the CMB pressure torque is due to the topography with the largest horizontal length scale. We calculate the minimum stratification for the topographic torque to produce discernible changes in the length-of-day.