| Summary: | 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 of === Earth, Ocean and Atmospheric Sciences, Department of === Graduate
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