Associated with non-steady magnetohydrodynamic (MHD) flow in the liquid metallic core of the Earth, with typical relative speeds of a fraction of a millimetre per second, are fluctuations in dynamic pressure of about 103 N m−2. Acting on the non-spherical core-mantle boundary (CMB), these pressure fluctuations give rise to a fluctuating net topographic torque Lt(t) (i=1, 2, 3)—where t denotes time—on the overlying solid mantle. Geophysicists now accept the proposal by one of us (RH) that Li-(t) makes a significant and possibly dominant contribution to the total torque Li*(t) on the mantle produced directly or indirectly by core motions. Other contributions are the ‘gravitational’ torque associated with fluctuating density gradients in the core, the ‘electromagnetic’ torque associated with Lorentz forces in the weakly electrically conducting lower mantle, and the ‘viscous’ torque associated with shearing motions in the boundary layer just below the CMB. the axial component L3*(t) of Li* (t) contributes to the observed fluctuations in the length of the day [LOD, an inverse measure of the angular speed of rotation of the solid Earth (mantle, crust and cryosphere)], and the equatorial components (Li* (t)) L* (t) contribute to the observed polar motion, as determined from measurements of changes in the Earth's rotation axis relative to its figure axis.
In earlier phases of a continuing programme of research based on a method for determining Li(t) from geophysical data (proposed independently about ten years ago by Hide and Le Mouël), it was shown that longitude-dependent irregular CMB topography no higher than about 0.5 km could give rise to values of L3(t) sufficient to account for the observed magnitude of LOD fluctuations on decadal time-scales. Here, we report an investigation of the equatorial components (L1(t), L2(t)) = L(t) of Li(t) taking into account just one topographic feature of the CMB—albeit possibly the most pronounced—namely the axisymmetric equatorial bulge, with an equatorial radius exceeding the polar radius by 9.5 ± 0.1 km (the mean radius of the core being 3485 2 km, 0.547 times that of the whole Earth). A measure of the local horizontal gradient of the fluctuating pressure field near the CMB can be obtained from the local Eulerian flow velocity in the ‘free stream’ below the CMB by supposing that nearly everywhere in the outer reaches of the core—the ‘polosphere’ (Hide 1995)—geostrophic balance obtains between the pressure gradient and Coriolis forces. the polospheric velocity fields used were those determined by Jackson (1989) from geomagnetic secular variations (GSV) data on the basis of the geostrophic approximation combined with the assumption that, on the time-scales of the GSV, the core behaves like a perfect electrical conductor and the mantle as a perfect insulator.
In general agreement with independent calculations by Hulot, Le Huy & Le Mouël (1996) and Greff-Lefftz & Legros (1995), we found that in magnitude L (t) for epochs from 1840 to 1990 typically exceeds L3(t) by a factor of about 10, roughly equal to the ratio of the height of the equatorial bulge to that strongly implied for irregular topography by determinations of L3(t) (see Hide et al. 1993). But L (t) still apparently falls short in magnitude by a factor of up to about 5 in its ability t o account for the amplitude of the observed time-series of polar motion on decadal time-scales (DPM), and it is poorly correlated with that time-series. So we conclude that unless uncertainties in the determination of the DPM time-series from observations-which we also discuss-have been seriously underestimated, the action of normal pressure forces associated with core motions on the equatorial bulge of the core-mantle boundary makes a significant but not dominant contribution to the excitation of decadal polar motion. Other geophysical processes such as the movement of groundwater and changes in sea-level must also be involved.