Penetration depth of flow perturbations into a stably stratified layer driven by rotating laterally heterogeneous convection

The present study investigates the penetrative effects of flow perturbations in a fluid layer with spatially varying thermal stratification. First, the theoretical estimation of the penetration depth (δ) for thermally damped wave-like flow disturbances is obtained in an unbounded fluid domain subject to background rotation and spatially heterogeneous thermal gradients. In particular, exact closed-form expressions for δ in an inviscid fluid are obtained with and without imposed magnetic fields. The derivations account for the role of the multiple physical constraints motivated from the geophysical scenario prevailing in the Earth's outer core. The role of heterogeneous buoyancy is characterized by a key parameter, Γ, defined as the ratio of horizontal to vertical thermal gradient. As Γ grows large, the penetration depth increases. The penetration characteristics are further explored in a bounded plane layer model using numerical simulations of rotating thermal convection with and without an imposed magnetic field. We impose thermally heterogeneous boundary conditions to mimic the Earth's core-mantle thermal interaction along with a partially stable stratification near the upper boundary. The inherent localization of convective instabilities, due to heterogeneous buoyancy, regionally enhances the penetration depth compared to homogeneous cases. The presence of the non-penetrative upper boundary in the plane layer simulations significantly reduces the penetration depth compared to the unbounded flow configuration. However, the fraction of the stable layer region penetrated by columnar convection increases with weakening of the stratification strength, supported by theoretical analysis. Implications are speculated for prevailing geophysical conditions in planetary cores.