Influence of Rotation on Fingering Convection in Planetary Cores

Abstract

Stably stratified layers are thought to develop at the top of the liquid metallic cores of many terrestrial planets. We consider the case where the thermal gradient is stable but the compositional gradient is unstable, a situation particularly relevant to Mercury. The strong contrast between molecular diffusivities of temperature and composition leads to fingering convection. We investigate this process using hydrodynamical simulations in a rotating spherical shell, systematically varying the stratification strength N relative to the rotation rate $Ω$. In all regimes, the primary fingering mode forms narrow, elongated structures that shift orientation from the rotation axis to the direction of gravity as $N^2/Ω^2$ exceeds 10. The fingers remain laminar, with transverse scales proportional to thermal stratification but independent of rotation. Fingering convection also drives secondary large-scale flows across most of the explored parameter space, producing diverse dynamics including zonal flows, hemispherical convection, axisymmetric poloidal bands, finger clusters, and toroidal gyres. In the rapidly-rotating regime, laterally inhomogeneous mixing generates zonal flows in thermo-compositional wind balance; zonal flow direction and amplitude depend on $N^2/Ω^2$, with amplitude weakening for strong stratification $N^2/Ω^2>10$. In the intermediate regime ($N^2/Ω^2\sim 1$), axisymmetric or spiraling poloidal bands emerge within the tangent cylinder, gradually overtaking the primary fingers. For stronger stratification, finger clusters and weak, large-scale density anomalies surrounded by toroidal gyres form in the upper domain. These diverse large-scale flows may interact with the dynamo-generated magnetic field in the deeper core, potentially influencing surface magnetic fields.