Extended Data Figure 5: Simplified sketch of the density transformation associated with scenarios S1 and S2.

a, Scenario S1 is the case of a uniform geothermal density sink or, equivalently, of a mixing-driven density flux that is uniform in the interior. Density loss occurs in a thin bottom boundary layer. The net density loss within a density layer, and therefore the dianeutral transport across it, is proportional to the layer’s incrop area. b, Scenario S2 is the case of bottom-enhanced turbulence where density loss in a thin bottom layer is compensated by an equal and opposite density gain above that layer. Density loss and density gain layers are sketched with equal thicknesses to illustrate this compensation: a density layer undergoes net density loss if the red area dominates over the blue area, and conversely. As an approximate rule, a density layer loses density in proportion to its incrop area but gains density in proportion to the incrop area of its underlying neighbour. Consequently, the larger the increase (or decrease) of incrop area with height, the larger the net density loss (or gain) of a density layer, and therefore the larger the net upwelling (or downwelling) transport across it.