Double-diffusive translation of Earth's inner core

The hemispherical asymmetry of the inner core has been interpreted as resulting from a high-viscosity mode of inner core convection, consisting in a translation of the inner core. A thermally driven translation, as originally proposed, is unlikely if the currently favoured high values of the thermal conductivity of iron at core conditions are correct. We consider here the possibility that inner core translation results from an unstable compositional gradient, which would develop either because the light elements present in the core become increasingly incompatible as the inner core grows, or because of a possibly positive feedback of the development of the F-layer on inner core convection. Though themagnitude of the destabilizing effect of the compositional field is predicted to be similar to or smaller than the stabilizing effect of the thermal field, the huge difference between thermal and chemical diffusivities implies that double-diffusive instabilities can still arise even if the net buoyancy increases upward. Using linear stability analysis and numerical simulations, we demonstrate that a translation mode can indeed exist if the compositional field is destabilizing, even if the temperature profile is subadiabatic, and irrespectively of the relative magnitudes of the composition and potential temperature gradients. The existence of this double diffusive mode of translation requires that the following conditions are met: (i) the compositional profile within the inner core is destabilizing, and remains so for a duration longer than the destabilization timescale (on the order of 200 Myr, but strongly dependent on the magnitude of the initial perturbation); and (ii) the inner core viscosity is sufficiently large, the required value being a strongly increasing function of the inner core size (e. g. 10(17) Pa s when the inner core was 200 km in radius, and similar or equal to 3 x 10(21) Pa s at the current inner core size). If these conditions are met, the predicted inner core translation rate is found to be similar to the inner core growth rate, which is more consistent with inferences from the geomagnetic field morphology and secular variation than the higher translation rate predicted for a thermally driven translation