A Tug-of-War Between Baroclinic Eddies and Convection: Implications for Icy Moon Oceans

In many geophysical and planetary environments, such as Earth's ocean and atmosphere as well as subsurface oceans of icy satellites, convection driven by bottom geothermal heating usually coexists with baroclinic eddies driven by lateral buoyancy/temperature gradients. These processes compete against each other, with convection destabilizing the stratification and baroclinic eddies re-stabilizing it, thereby controlling whether the bottom heat flux is significantly redistributed as it is transmitted to the upper surface. Using scaling analysis and numerical simulations, we show that a stratified layer persists near the upper surface up to ${\rm Ra}_{v}\sim {\rm Ra}_h^{5/2}$, where ${\rm Ra}_h\equiv Δb_0/(L_zf^2)$ measures the imposed upper-surface buoyancy contrast $Δb_0$ and ${\rm Ra}_v\equiv B_0/(L_z^2f^3)$ measures the strength of the bottom buoyancy flux $B_0$, $L_z$ is the domain depth and $f$ is the Coriolis parameter. For ${\rm Ra}_v<{\rm Ra}_h^{5/2}$, baroclinic eddies dominate over convection, maintain the upper stratified layer, and completely deflect the bottom buoyancy/heat input into meridional transport. In contrast, when ${\rm Ra}_v>{\rm Ra}_h^{5/2}$, convective plumes penetrate the stratification and transport buoyancy/heat vertically with negligible deflection. Building on these results, we further propose a scaling law for the meridional buoyancy/heat transport in this system. Applications to icy satellites are discussed.