The strength and efficiency of thermal and compositional convection in the geodynamo

Abstract

The evolution of the Earth's outer core is calculated theoretically by assuming that the fluctuations about a vigorously convecting, well-mixed, isentropic and hydrostatic mean state are small. The global energy equation describes the evolution of the mean state, but contains no information about the division between convective and diffusive transport of heat or composition within the core itself. As the diffusive transport of either heat or composition makes no contribution to the dynamo, estimates of the dynamo power must be derived by explicit consideration of the correlation of small density fluctuations with the large convective velocities. By such consideration, the dynamo power is shown to be equal to the integrated thermal and compositional buoyancy flux, which is calculated from the requirement that the mean state remain isentropic and well mixed. The resulting new and simple expression for the dynamo efficiency has an easily understood physical interpretation in terms of Carnot-style redistribution of heat and mass in the core, though it takes full account of both thermal and compositional effects and the evolution of the mean state. Once the equation of state and thermodynamic parameters are given, the dynamo power can be evaluated readily and explicity. Analytic solutions based on a simple example equation of state show that the relative importance of thermal and compositional convection depends on the size of the inner core and the amount by which the heat flux across the core-mantle boundary (CMB) exceeds that which can be conducted up the core adiabat. Thermal convection was dominant in the early Earth when the inner core was small and the Earth was probably cooling rapidly. Estimates of the present-day heat loss across the CMB suggest that thermal convection now contributes about 20% of the dynamo power and compositional convection about 80%. As a result of the release of latent heat at the inner-core boundary, thermal convection can make a net positive contribution to the dynamo power even if the heat flux at the CMB is subadiabatic.