Abstract
An initially resting ocean of stratification N is considered, subject to buoyancy loss at its surface of magnitude B0 over a circular region of radius r, at a latitude where the Coriolis parameter is f. Initially the buoyancy loss gives rise to upright convection as an ensemble of plumes penetrates the stratified ocean creating a vertically mixed layer. However, as deepening proceeds, horizontal density gradients at the edge of the forcing region support a geostrophic rim current, which develops growing meanders through baroclinic instability. Eventually finite-amplitude baroclinic eddies sweep stratified water into the convective region at the surface and transport convected water outward and away below, setting up a steady state in which lateral buoyancy flux offsets buoyancy loss at the surface. In this final state quasi-horizontal baroclinic eddy transfer dominates upright “plume” convection.
By using “parcel theory” to consider the energy transformations taking place, it is shown that the depth, hfinal at which deepening by convective plumes is arrested by lateral buoyancy flux due to baroclinic eddies, and the time tfinal it takes to reach this depth, is given by
both independent of rotation. Here γ and β are dimensionless constants that depend on the efficiency of baroclinic eddy transfer. A number of laboratory and numerical experiments are then inspected and carried out to seek confirmation of these parameter dependencies and obtain quantitative estimates of the constants. It is found that γ = 3.9 ± 0.9 and β = 12 ± 3.
Finally, the implications of our study to the understanding of integral properties of deep and intermediate convection in the ocean are discussed.
