A 3-DIMENSIONAL CONVECTIVE DYNAMO SOLUTION WITH ROTATING AND FINITELY CONDUCTING INNER-CORE AND MANTLE

We present the first three-dimensional (3D), time-dependent, self-consistent numerical solution of the magnetohydrodynamic (MHD) equations that describe thermal convection and magnetic field generation in a rapidly rotating spherical fluid shell with a solid conducting inner core. This solution, which serves as a crude analog for the geodynamo, is a self-sustaining supercritical dynamo that has maintained a magnetic field for three magnetic diffusion times, roughly 40000 years. Fluid velocity in the outer core reaches a maximum of 0.4 cm s(-1), and at times the magnetic field can be as large as 560 gauss. Magnetic energy is usually about 4000 times greater than the kinetic energy of the convection that maintains it. Viscous and magnetic coupling to both the inner core below and the mantle above cause time-dependent variations in their respective rotation rates; the inner core usually rotates faster than the mantle and decadal variations in the length of the day of the mantle are similar to those observed for the Earth. The pattern and amplitude of the radial magnetic field at the core-mantle boundary (CMB) and its secular variation are also similar to the Earth's. The maximum amplitudes of the longitudinally averaged temperature gradient, shear flow, helicity, and magnetic field oscillate between the northern and southern hemispheres on a time scale of a few thousand years. However, only once in many attempts does the field succeed in reversing its polarity because the field in the inner core, which has the opposite polarity to the field in most of the outer core, usually does not have enough time to reverse before the field in the outer core changes again. One successful magnetic field reversal occurs near the end of our simulation.