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Electromagnetic coupling between the fluid core and its solid neighbours Dumberry, Mathieu


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.

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