Heat Flow and Boundary Heterogeneity in Rotating Convection

Abstract: Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence global diagnostics of core convection when the Rayleigh number, $Ra$, is weakly supercritical; however, little is known about the strongly supercritical regime appropriate for planets. We perform numerical simulations of rapidly rotating convection in a spherical shell geometry and impose two patterns of boundary heat flow heterogeneity: a hemispherical $Y_1^1$ spherical harmonic pattern; and one derived from seismic tomography of Earth's lower mantle. We consider Ekman numbers $10^{-4} \le E \le 10^{-6}$, flux-based Rayleigh numbers up to $\sim800$ times critical, and Prandtl number unity. The amplitude of the lateral variation in heat flux is characterised by $q_{\rm L}^*=0, 2.3, 5.0$, the peak-to-peak amplitude of the outer boundary heat flux divided by its mean. We find that the Nusselt number, $Nu$, can be increased by up to $\sim25$\% relative to the equivalent homogeneous case due to boundary-induced correlations between the radial velocity and temperature anomalies near the top of the shell. The $Nu$ enhancement tends to become greater as the amplitude and length scale of the boundary heterogeneity are increased and as the system becomes more supercritical. This $Ra$ dependence can steepen the $Nu \propto Ra^\gamma$ scaling in the rotationally dominated regime, with $\gamma$ for our most extreme case approximately $20\%$ greater than the equivalent homogeneous scaling. Therefore, it may be important to consider boundary heterogeneity when extrapolating numerical results to planetary conditions.