Penetration of boundary-driven flows into a rotating spherical thermally stratified fluid

Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), 10(-3) <= S <= 10(4), a buoyancy parameter (the strength of applied boundary heat-flux anomalies), 10(-2) <= B <= 10(6), and the Ekman number (ratio of viscous to Coriolis forces), 10(-6) <= E <= 10(-4). We find both steady and time-dependent solutions and delineate the regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low S regime, in which buoyancy dominates the dynamics, and a high S regime, in which stratification dominates. For the low-S regime, we find that the characteristic flow speed scales as B-2/3, whereas for high-S, the radial and horizontal velocities scale respectively as u(r) similar to S-1, u(h) similar to S-3/4 B-1/4 and are confined within a thin layer of depth (SB)(-1/4) at the outer edge of the domain. For the Earth, if lower mantle heterogeneous structure is due principally to chemical anomalies, we estimate that the core is in the high-S regime and steady flows arising from strong outer boundary thermal anomalies cannot penetrate the stable layer. However, if the mantle heterogeneities are due to thermal anomalies and the heat-flux variation is large, the core will be in a low-S regime in which the stable layer is likely penetrated by boundary-driven flows.