Equations governing convection in earth's core and the geodynamo

Convection in Earth's fluid core is regarded as a small deviation from a well-mixed adiabatic state of uniform chemical composition. The core is modeled as a binary alloy of iron and some lighter constituent, whose precise chemical composition is unknown but which is here assumed to be FeAd, where Ad = Si, O or S. The turbulent transport of heat and light constituent is considered, and a simple ansatz is proposed in which this is modeled by anisotropic diffusion. On this basis, a closed system of equations and boundary conditions is derived that governs core convection and the geodynamo. The dual (thermal + compositional) nature of core convection is reconsidered. It is concluded that compositional convection may not dominate thermal convection, as had previously been argued by Braginsky (Soviet Phys. Dokl., v. 149, p. 8, 1963; Geomag, and Aeron., v. 4, p. 698, 1964), but that the two mechanisms are most probably comparable in importance. The key parameters leading to this conclusion are isolated and estimated. Their uncertainties, which in some cases are large, are highlighted. The energetics and efficiency of the geodynamo are reconsidered and re-estimated. Arguments are advanced that indicate that the mass fraction of the light constituent in the solid inner core may not be small compared with that in the outer core, e.g. about 60%. This tends to favor silicon or sulfur over oxygen as the principal light alloying constituent.