Anomalous rotation of the inner core and the toroidal magnetic field

We use numerical calculations of magnetic induction by axisymmetric motions in a spherical Shell of conducting fluid to investigate the relationship between the Earth's toroidal magnetic field and the time-dependent anomalous rotation of the solid inner core. We compute the induced toroidal magnetic field and inner core rotation maintained by the interaction of time-independent, axisymmetric outer core fluid flow with models of the poloidal magnetic field. Three possible models of-the azimuthal flow in the outer core are investigated: two thermal wind flows inside the tangent cylinder (predicted by some numerical models of the geodynamo) and a columnar flow outside the inner core tangent cylinder inferred from the geomagnetic westward drift. Results indicate that electromagnetic torques tightly couple the inner core rotation to the fluid motion. Electromagnetic spin-up of the inner core occurs through damped torsional oscillations with periodicity near 4 years depending on the strength of the poloidal magnetic field. In steady state the thermal winds inside the tangent cylinder generate a peak toroidal field of 25 mT accompanying a prograde inner core rotation rate of 1 degrees/yr. In contrast, the columnar westward drift model generates toroidal field with peak intensity near 4 mT and a small, retrograde anomalous inner core rotation of -0.013 degrees/yr. The weak retrograde motion of the inner core produced by electromagnetic coupling to the westward drift cannot explain the seismically inferred prograde anomalous rotation.