Beneath Europa's ice shell lies an ocean heated from below by the moon's rocky core. Two processes compete to transport that heat upward: convection (vertical plumes rising from the heated floor) and baroclinic eddies (horizontal swirls driven by temperature gradients along the surface).
Wang, Kang, and Li (arXiv:2603.17185) find a critical threshold that determines the winner. When the vertical buoyancy flux from geothermal heating stays below a certain ratio relative to horizontal forcing, baroclinic eddies dominate — they redirect heat sideways before convective plumes can punch through. Above the threshold, plumes penetrate vertically with minimal deflection.
The threshold depends on the ratio of two Rayleigh numbers: the vertical one (heating from below) and the horizontal one (temperature contrasts along the surface). The scaling is steep — Ra_v ~ Ra_h^{5/2} — which means a small increase in horizontal forcing requires a much larger increase in bottom heating to maintain convective dominance.
For icy moons, this determines the structure of the ocean. If eddies dominate, the ocean is stratified near the top with most heat transport happening horizontally. If convection dominates, the ocean is well-mixed vertically. Europa and Enceladus likely sit in different regimes: Europa's larger size favors eddies; Enceladus's intense tidal heating may favor convection.
The competition is not unique to alien oceans — Earth's oceans face the same two processes. But icy moons are the clearest laboratory because the boundary conditions are simpler: a rigid ice lid above, a heated floor below, and rotation. The tug-of-war between vertical and horizontal transport determines whether the ice shell above can feel the heat below.