What can the observed rotation of the Earth's inner core reveal about the state of the outer core?

Abstract

The discovery that the Earth's inner core is rotating relative to the mantle has prompted a number of authors to reinvestigate the dynamics of inner core rotation. These models include a highly idealized analytical one by Aurnou, Brito and Olson (1996), as well as a fully 3-D numerical one by Glatzmaier and Roberts (1996). In this work I present a model intermediate between these two extremes. In particular, I retain the simplicity of the model of Aurnou et al. by kinematically prescribing a thermal wind and poloidal magnetic field. By doing so it is possible to vary the strengths of these quantities at will, and thereby explore the dependence of the inner core's rotation rate on them more thoroughly than in the model of Glatzmaier and Roberts, where these quantities emerge as part of the solution, and one therefore has far less control over their strengths. However, as in the model of Glatzmaier and Roberts, the full back-reaction of the magnetic field on the fluid flow in the outer core is included. It is found that if one includes this effect, the relationship between the inner core's rotation rate and the strength of the thermal wind is more complicated than that found by Aurnou et al., who did not include it. As a result, while the observed rotation of the inner core certainly gives a rigorous lower bound on the maximum difference in angular velocity throughout the outer core, that maximum difference could be as much as an order of magnitude greater. Finally, it is also pointed out that, because of the particular nature of the torque balance that determines the inner core's rotation rate, it is difficult, if not impossible, to use that observed rate to obtain precise bounds on the magnetic field strength deep within the core.