Top-heavy double-diffusive convection with core-mantle boundary heat flux variations

The geomagnetic field is sustained by thermochemical convection in Earth’s outer core. Crystallization of the solid inner core releases latent heat and light elements, providing both thermal and chemical buoyancy sources. Most geodynamo simulations use the codensity approach, ignoring the vastly different diffusivities and different boundary conditions for the thermal and chemical fields and thus cannot capture double-diffusive effects. In this study, we consider a numerical convection model of a Boussinesq mixture of light elements in a heavy fluid confined within a rotating spherical shell. The governing parameters are the Ekman number (𝐸 = 2 × 10⁻⁵), a non-dimensional measure of the rotation rate, the thermal and chemical flux Rayleigh numbers (𝑅𝑎_𝑇 = 9 × 10⁶ − 1.2 × 10⁸ and 𝑅𝑎_𝜉 = 3 × 10⁶ − 5 × 10¹⁰), representing the non-dimensional thermal and chemical forcing, and the thermal and chemical Prandtl numbers (𝑃𝑟_𝑇 = 1 and 𝑃𝑟_𝜉 = 10), that are fluid properties. We have performed a detailed analysis of the force balance that emerges within these simulations. We find a transition from a thermal wind to a chemical wind balance with increasing chemical forcing in the azimuthally averaged ”mean” forces in the radial direction. The transition is found to occur at buoyancy ratio, Λ = (𝑅𝑎_𝑇 /𝑃𝑟_𝑇 )/(𝑅𝑎_𝜉 /𝑃𝑟_𝜉 ) ≃ 1. However, the corresponding ”fluctuating” balance is quasi-geostrophic in all directions. The analysis lets us locate the geophysically relevant ”rapidly rotating” regime in this parameter space.

We proceed by imposing a laterally heterogeneous thermal flux at the core-mantle boundary (CMB) in our rapidly rotating double-diffusive simulations. Recent thermally-driven simulations with lateral variations in CMB heat flux produce local regions with a subadiabatic thermal gradient near the CMB (Mound et al., 2019), termed as regional inversion lenses (RILs). This may reconcile the conflicting inferences about the possibility of a globally stratified layer at the top of the core (Kaneshima 2018; Gastine et al. 2020), by accommodating the possibility of both stable and unstable regions. Our goal is to assess the effect of chemical buoyancy on the RILs. The parameter space now also includes the pattern and amplitude of lateral variation in the CMB heat flux. A standard ’tomographic’ pattern, as suggested by seismic measurements (Masters et al., 1996), has been used in these simulations. The amplitude is characterized as 𝑞^∗ = (𝑞_𝑚𝑎𝑥 − 𝑞_𝑚𝑖𝑛)/𝑞_𝑎𝑣𝑔 where 𝑞_𝑚𝑎𝑥, 𝑞_𝑚𝑖𝑛, and 𝑞_𝑎𝑣𝑔 are the maximum, minimum and horizontally averaged heat flux through the CMB. We study the RILs by varying the lateral heterogeneity with 𝑞∗ = {1, 2.3, 5} and buoyancy ratios with Λ = 400-0.01. These RILs are characterized by their strength, measured by a characteristic Brunt-Väisälä frequency (𝑁). Their thickness (𝐿) is measured as the distance of the point of neutral stability from CMB, and the chemical anomaly (𝛿𝜉 ) represents the difference in chemical composition across the lenses. The scaling dependence of these quantities (Mound & Davies, 2020) on the chemical forcing has been explored to extrapolate their values for Earth-like parameters.