nondim-slurry_v0.1

Python module to solve the 1D, steady, spherical slurry system outlined in Wong et al. (2021) (see also Wong et al. 2018). Seismic observations of a slowdown in P wave velocity at the base of Earth’s outer core suggest the presence of a stably-stratified region known as the F-layer. This raises an important question: how can light elements that drive the geodynamo pass through the stably-stratified layer without disturbing it? We consider the F-layer as a slurry containing solid particles dispersed within the liquid iron alloy that snow under gravity towards the inner core. We present a regime diagram showing how the dynamics of the slurry F-layer change upon varying the key parameters: Péclet number (Pe), the ratio between advection and chemical diffusion; Stefan number (St), the ratio between sensible and latent heat; and Lewis number (Le), the ratio between thermal and chemical diffusivity. We obtain four regimes corresponding to stable, partially stable,unstable and no slurries. No slurry is found when the heat flow at the base of the layer exceeds the heat flow at the top, while a stably-stratified slurry arises when advection overcomes thermal diffusion (Pe>Le) that exists over a wide range of parameters relevant to the Earth’s core. Our results estimate that a stably-stratified F-layer gives a maximum inner-core boundary (ICB) body wave density jump of ∆ρ_bod ≤ 534 kg/m^3 which is compatible with the lower end of the seismic observations where 280 ≤ ∆ρ_bod ≤ 1,100 kg/m^3 is reported in the literature. With high thermal conductivity the model predicts an inner core age between 0.6 and 1.2 Ga, which is consistent with other core evolution models. Our results suggest that a slurry model with high core conductivity predicts geophysical properties of the F-layer and core that are consistent with independent seismic and geodynamic calculations.JW acknowledges support from the Fondation Simone and Cino Del Duca of Institut de France and the Engineering and Physical Sciences Research Council (EPSRC) Centre for Doctoral Training in Fluid Dynamics (EP/L01615X/1). CJD is supported by the Natural Environment Research Council (NERC) Independent Research Fellowship (NE/L011328/1)