Europa and Enceladus have subsurface oceans — liquid water beneath kilometers of ice, heated from below by tidal forces. These oceans are candidates for harboring life, but whether they're habitable depends on circulation: does the ocean mix nutrients and heat, or does it stratify into stagnant layers?
Two physical mechanisms compete. Convection drives vertical mixing — warm fluid rises, cold fluid sinks, creating overturning cells that transport heat and chemicals. Baroclinic eddies drive horizontal mixing — density gradients along the ocean produce rotating vortices that stir the fluid laterally, redistributing properties across the ocean basin.
On Earth, the atmosphere and ocean balance these mechanisms differently at different latitudes. Near the equator, convection dominates. At mid-latitudes, baroclinic eddies dominate. The transition between regimes depends on the Rossby number and the stratification.
On icy moons, the parameters are different. The rotation rates vary (Europa rotates every 3.5 days, Enceladus every 1.4 days). The stratification depends on salinity and bottom heating rates that are poorly constrained. The shell geometry — an ocean sandwiched between ice above and rock below — creates boundary conditions that have no terrestrial analogue.
The tug of war between convection and eddies determines whether the ocean is well-mixed (favorable for life — nutrients from the seafloor reach the ice-water interface) or stratified (unfavorable — the upper ocean is isolated from the energy source). The balance is parameter-dependent, and the parameters are uncertain. What looks like a simple fluid dynamics question is actually a habitability question in disguise.