Thermochemical models of outer core convection with heterogeneous core-mantle boundary heat flux

TL;DR

This paper demonstrates that thermochemical convection in a rotating spherical shell can generate both chemically and thermally stabilized regions beneath the CMB, including regional inversion lenses (RILs) when lateral CMB heat flux variations are imposed. Using 92 numerical models with $E=10^{-5}$, $ ilde{Ra}_T$ up to 4000 and $ ilde{Ra}_\xi$ up to 10^5, with $Pr_T=1$ and $Pr_\xi=10$, the authors show LEA below the CMB drives chemically stable regions, while heterogeneity in outer-boundary heat flux drives RILs that are typically ~100 km thick and stronger with greater thermal forcing. The key contributions are (i) establishing the coexistence and competition between LEA-driven chemical stability and thermally driven RILs, (ii) quantifying how RIL thickness and strength scale with $ ilde{Ra}_T$ and boundary heterogeneity $q^*$, and (iii) connecting these dynamics to seismic and geomagnetic observables, suggesting a geophysically plausible top-core stratification compatible with both observations and dynamo behavior. The findings imply a more nuanced upper-core structure than a global stable layer, with potential implications for interpreting seismic tomography and geomagnetic secular variation.

Abstract

Thermochemical convection in Earth's outer core is driven by the crystallisation of the inner core that releases latent heat and light elements. A key question in core dynamics is whether a stable layer exists just below the core-mantle boundary. Recent core convection simulations, accounting for CMB heterogeneities, propose locally stable regions (or regional inversion lenses, RILs) rather than a global layer, allowing both stable and unstable regions to coexist. In this study, we consider a suite of numerical simulations of thermal, chemical, and thermochemical convection models focussed on Ekman number ($E=10^{-5}$) with thermal and chemical flux Rayleigh numbers $\widetilde{Ra}_T=30-4000$ and $\widetilde{Ra}_C=30-100000$, and thermal and chemical Prandtl numbers $Pr_T=1$ and $Pr_ξ=10$. Analysis of purely chemical models reveals light element accumulation (LEA) below the CMB, resulting in either locally stable regions near the poles or global layers, depending on the strength of chemical forcing. These chemically stratified regions persist in our thermochemical models even if the thermal field is fully destabilising. The addition of a heterogeneous CMB heat flux leads to the formation of RILs driven by thermal stratification. Stable regions in these thermochemical models have varying locations, properties, and morphologies depending on whether thermal or chemical convection dominates. In the investigated parameter range, these RILs are O(100 km) thick, and their strength and thickness generally increase with the strength of thermal driving; they are comparatively less sensitive to the strength of chemical driving. Our simulations reveal a diverse range of possible stable regions and/or a global layer at the top of Earth's core, with a seismically plausible range of thickness and strength, which may also have a signature in geomagnetic observations.

Figures (13)

• Figure 1: Regimes of force balance in homogeneous models. The symbol shapes indicate purely thermal (diamonds), purely chemical (stars) and thermochemical (left/right triangles). The symbols are coloured by the fluctuating curled force ratio $CF_{I/C}$, indicating the role of inertia in the force balance relative to the Coriolis force. Open symbols are used for fluctuating force ratio $F_{I/C}\geq0.1$, while filled symbols indicate $F_{I/C}<0.1$. The thermochemical models are classified with the ratio of thermal to chemical buoyancy $A_{T/\xi} \leq 1$ (left triangles) and $A_{T/\xi} >1$ (right triangles), respectively. The dashed red lines at the lower left corner indicate the critical lines for the onset of convection. Blue and red squares indicate, respectively, the example chemically-dominated and thermally-dominated simulations discussed in the text.
• Figure 2: Scalar fields and their gradients in homogeneous simulations. The equatorial, meridional and spherical ($r=0.54$) surfaces are colored by thermal anomaly (a,d), chemical anomaly (b,e), and radial velocity (c,f). The contour colours indicate hot (red) or cold (blue) fluid in (a,d), high (orange) or low (purple) concentration of light elements in (b,e), and positive (red) or negative (blue) radial velocity in (c,f). The green iso-volume depicts time-averaged chemically stable regions with $\partial \xi/\partial r>0$ in (b,e), and convectively stable regions with $N^{2}/4\Omega^{2}>0$ in (c,f). Chemically dominated convection (a,b,c) at $\widetilde{Ra}_T=90$ and $\widetilde{Ra}_\xi=30000$, compared to thermally dominated convection (d,e,f) at $\widetilde{Ra}_T=1200$ and $\widetilde{Ra}_\xi=300$. To avoid obscuring interior structure, the stable regions (green isovolume) are clipped in the front hemisphere.
• Figure 3: Scalar fields and their gradients in heterogeneous simulations. The interpretations of the contour colour and isovolumes are the same as in Figure \ref{['fig:homog']}. These heterogeneous simulations for $q^{*}=5$ have otherwise the same parameters as their homogeneous counterparts in Figure \ref{['fig:homog']}. To avoid obscuring interior structures, the time-averaged stable regions (green isovolume) are clipped in the entire front hemisphere in the middle panels, and for $z>0.6$ in panel (f).
• Figure 4: Variation of $N^{2}/4\Omega^{2}$ with depth below CMB near the top of the core for homogeneous (a,b) and heterogeneous (c,d) models, averaged around various locations (see Figure \ref{['fig:geometry']} in Appendix \ref{['app:SI']}) for models with compositionally dominated convection (a,c) at $\widetilde{Ra}_T=90$ and $\widetilde{Ra}_\xi=30000$, and thermally dominated convection (b,d) at $\widetilde{Ra}_T=1200$ and $\widetilde{Ra}_\xi=300$.
• Figure 5: Regimes of thermochemical stability in the heterogeneous models. The symbols are colored by their thickness (a) and strength (b). The thickness/strength in the colorbar represents the maximum value among the locally averaged profiles we considered (e.g see Figure \ref{['fig:tomog_prof']}). The globally averaged profile exhibits stratification in the model represented by a circle. A complete global layer of stratification is found for the model indicated by a diamond symbol.