A buoyancy profile for the Earth's core

We investigate the thermal and chemical buoyancy forces that drive convection in the Earth's liquid outer core and derive a radial buoyancy profile that can be used in geodynamo models. We assume the core is well mixed, adiabatic and cools as a result of mantle convection. The buoyancy profile is developed for a Boussinesq fluid and incorporates secular cooling, latent heat release at the inner core boundary, radiogenic heating, the effect of the adiabat, and compositional buoyancy due to inner core freezing. Surprisingly, these complex effects can be modelled accurately by a simple combination of bottom heating and near-uniform heat sinks, which is implemented using a cotemperature formulation that converts compositional effects into effective thermal effects. The relative importance of internal and bottom heating is then defined by just two parameters, the cooling rate at the core-mantle boundary (CMB) and the uniform rate of internal radiogenic heat production, both of which can be obtained from core evolution calculations. We vary these parameters in geodynamo models and compare basic features of the generated fields with the geomagnetic field; in this manner we link core evolution models, geodynamo simulations and geomagnetic observations. We consider three end-member scenarios for core evolution: (1) rapid cooling and a young inner core; (2) moderate cooling and neutral stability at the CMB; (3) slow cooling and enough radiogenic heating to allow the inner core to be 3.5 Gyr old. We find that compositional buoyancy dominates thermal buoyancy everywhere except near the CMB, even with large amounts of radiogenic heating, and buoyancy forces are far larger at depth than higher up. Reducing the cooling rate and increasing radiogenic heating reduces the drop in the superadiabatic gradient between the inner and outer boundaries: for rapid cooling the drop is by a factor 50; for slow cooling it is a factor of 5. We demonstrate the effects of these different buoyancy profiles in numerical simulations as a function of the Rayleigh number. At low Rayleigh number the internal velocity and magnetic fields vary between the core evolution scenarios, but these differences do not affect the surface field. Significant differences in the surface field emerge when the Rayleigh number is sufficiently large. For rapid cooling we find dipolar magnetic fields in the time average that reverse and are dominated by large-scale features at high latitudes. Moderate cooling results in magnetic fields that are stable and dominantly dipolar. Slow cooling produces multipolar magnetic fields that reverse very frequently. This preliminary study suggests that the generated fields are sufficiently different that geodynamo simulations together with geomagnetic observations could be used to discriminate between different core evolution scenarios.