The dynamics of Earth’s inner core depends critically on whether it is stably stratified or unstably stratified. We propose here a general analysis of the thermal evolution of the inner core. Whether the geotherm in the inner core is superadiabatic or not depends on the inner core solidification rate, on the thermal diffusivity of iron at inner core conditions, and on the ratio of the Clapeyron slope to the adiabatic gradient in the inner core. The temperature field within the inner core can be destabilizing—and could drive convection—if the growth of the inner core is fast enough. The effect of radiogenic heating is probably small, and, perhaps surprisingly, can even stabilize the inner core against convection. The uncertainties are such that it is not possible at present to conclude about the likelihood of thermal convection in the inner core, but recent estimates of the Core–Mantle Boundary (CMB) heat flux and inner core conductivity favour convection. Thermal convection is more likely early in the inner core history, a consequence of the secular decrease in cooling rate of the core. In addition, solidification-induced partitioning of the light elements may induce a stable density stratification within the inner core.
We develop a numerical model of thermochemical convection in a growing inner core, which couples the evolution and dynamics of the inner core with the thermal and compositional evolution of the outer core. Melting and crystallization associated with deformation of the Inner Core Boundary (ICB) would be of importance for the style of convection if the viscosity is large, but we focus here on the case of low viscosity for which phase change associated with dynamic topography at the ICB is expected to play a secondary role. In this regime, convection is typical of high Rayleigh number internally heated convection, with cold plumes falling from the ICB.
Several possible scenarios can lead to a layered inner core, either because of cessation of thermal convection due to the decrease in cooling rate of the core, or because of a compositional stratification which can confine convection in the deep inner core, or stabilize the whole inner core. For each of these scenarios, it is possible to find plausible sets of parameters (inner core age, viscosity, magnitude of the compositional stratification) for which the radius at which convection stops corresponds to the radius of the seismically inferred innermost inner core.