The strength of gravitational core-mantle coupling

Gravitational coupling between Earth's core and mantle has been proposed as an explanation for a 6 year variation in the length-of-day (ΔLOD) signal and plays a key role in the possible superrotation of the inner core. Explaining the observations requires that the strength of the coupling, Γ, falls within fairly restrictive bounds; however, the value of Γ is highly uncertain because it depends on the distribution of mass anomalies in the mantle. We estimate Γ from a broad range of viscous mantle flow models with density anomalies inferred from seismic tomography. Requiring models to give a correlation larger than 70% to the surface geoid and match the dynamic core-mantle boundary ellipticity inferred from Earth's nutations, we find that 3 × 10(19)<Γ<2 × 10(20) N m, too small to explain the 6 year ΔLOD signal. This new constraint on Γ has important implications for core-mantle angular momentum transfer and on the preferred mode of inner core convection

The Influence of a Fluid Core and a Solid Inner Core on the Cassini State of Mercury

We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arcmin. EM coupling is stronger than viscous coupling at the inner core boundary and, if the core magnetic field strength is above 0.3 mT, locks the fluid and solid cores into a common precession motion. Because of the strong gravitational coupling between the mantle and inner core, the larger the inner core is, the more this co-precessing core is brought into an alignment with the mantle, and the more the obliquity of the polar moment of inertia approaches that expected for a rigid planet. The misalignment between the polar moment of inertia and mantle spin axis increases with inner core size, but is limited to 0.007 arcmin. Our results imply that the measured obliquities of the mantle spin axis and polar moment of inertia should coincide at the present-day level of measurement errors, and cannot be distinguished from the obliquity of a rigid planet.Comment: 33 pages, 7 figure

Electromagnetic coupling between the fluid core and its solid neighbours

At low-frequency, the nearly geostrophic force balance in the fluid core constrains axisymmetric fluid motions to be purely azimuthal and independent of position along the rotation axis. Fluid motions can thus be described by a set of concentric rigid cylinders, which are free to rotate about their common axis. When these cylinders are coupled by a magnetic field, the associated restoring forces give rise to torsional oscillations. These waves are thought to cause the observed fluctuations in the length of day by transferring angular momentum to the mantle and the inner core. The theory of torsional oscillations assumes that the stresses at the fluid-solid boundaries, which transfer angular momentum, do not alter the rigid nature of the fluid cylinders. This assumption is probably valid at the base of the mantle where the magnetic field is not large enough to alter the geostrophic balance in the fluid near the boundary. However, it is not valid at the inner core boundary (ICB) where higher field strengths are likely to perturb the geostrophic balance. In this case, the Lorentz force has to be retained in the momentum balance. A complete analytical solution is given for the influence of Lorentz forces in the core. The model problem involves a conducting and rotating fluid between two plane conducting boundaries in the presence of a background magnetic field. The solution gives us a clear view of how boundary layers form near the solid and how the coupling to the mantle and the inner core occurs.' More importantly, we can directly see how the inclusion of Lorentz forces alters the velocity from rigid rotation and how this velocity differs from that obtained with the torsional oscillation theory. For cylinders that terminate on the inner core, it is found that the rigid rotations are perturbed for a range of background magnetic field strength and frequencies. At decade periods, there is insufficient inertia to disrupt rigid rotations. However, for annual fluctuations, departures in the fluid velocity from rigid rotations are significant, which implies that the Lorentz force can not be neglected in the dynamics of the fluid core when calculating the electromagnetic coupling at the ICB.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat