Coupled convective and morphological instability of the inner core boundary of the Earth

Taking into account the convective heat and mass transfer in the liquid phase, we develop the linear theory of morphological instability of the solid–liquid interface under solidification conditions typical for the inner core. The generalized stability criterion obtained includes analytic results of the recent theories [Shimizu, H., Poirier, J.P., Le Mouël, J.L., 2005. Phys. Earth Planet. Int. 151, 37–51; Deguen, R., Alboussière, T., Brito, D., 2007. Phys. Earth Planet. Int. 164, 36–49], where the role of convection on stability was only partially studied. The generalized criterion shows that both regimes of stable and unstable solidification are quite plausible if the growth rate of the inner core is episodic and variable. This stability criterion and the criterion of constitutional supercooling demonstrate that there are two possible solidification scenarios: “constitutional supercooling and morphological stability” and “constitutional supercooling and morphological instability”. These crystallization regimes are described by means of the slurry and mushy layer theories. Two models of solidification in the presence of convective motions near the inner core boundary with the slurry and mushy layers are considered. New analytical solutions of these nonlinear models with two moving boundaries of the phase transition domain in the steady-state crystallization regime are found.