Analytical computation of the total topographic torque at the core–mantle boundary and its impact on nutations

SUMMARY In this paper, we examine the dynamic pressure torque acting on a bumpy core–mantle boundary (CMB) at diurnal timescale in a frame tied to the planet. This torque possibly contributes to the CMB coupling constants determined from nutation observations and could affect the interpretation of these constants in terms of different CMB coupling mechanisms. We revisit the work of Wu & Wahr (1997) who have used seismic estimates for the topography at the CMB and computed the associated pressure torque effect on nutations. These authors showed that some topography wavelengths can lead to amplifications in nutations. For example, they found that the effects on the retrograde annual nutation can be at the milliarcsecond level for a degree-5 spherical harmonics of the topography. While Wu & Wahr (1997) only go up to degree 6 in their development in spherical harmonics and use a numerical technique, we go up to degree 20 and employ an analytical approach to solve the equations and to further study the Earth’s nutations. The approach is similar to the one we used for the effects of the pressure torque on the tidal variations of the length of day (a companion paper, Puica et al. 2023). Unlike the numerical approach, this has the advantage of highlighting the mathematical dependencies between the different spherical harmonics involved in the development of the topographic torque and to highlight the frequency dependence of the results and thereby the possible resonances with inertial waves. By doing so, we can isolate and estimate the magnitude of the influence of each topographic coefficient on nutation. We show that only the core flattening may have an important role on nutation and that the other large wavelengths of the topography have a very small contribution, less than that obtained by Wu & Wahr (1997).