DYNAMICS OF ISOLATED CONVECTIVE REGIONS IN THE OCEAN

An initially resting ocean of stratification N is considered, subject to buoyancy loss at its surface of magnitude B-0 over a circular regio n of radius r, at a latitude where the Coriolis parameter is f. Initia lly 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, whi ch develops growing meanders through baroclinic instability. Eventuall y finite-amplitude baroclinic eddies sweep stratified water into the c onvective region at the surface and transport convected water outward and away below, setting up a steady state in which lateral buoyancy fl ux offsets buoyancy loss at the surface. In this final state quasi-hor izontal baroclinic eddy transfer dominates upright ''plume'' convectio n. By using ''parcel theory'' to consider the energy transformations t aking place, it is shown that the depth, h(final), at which deepening by convective plumes is arrested by lateral buoyancy flux due to baroc linic eddies, and the time t(final) it takes to reach this depth, is g iven by h(final) = gamma (B(0)r)(1/3)/N, t(final) = beta (r(2)/B-0)(1/ 3), both independent of rotation. Here gamma and beta are dimensionles s constants that depend on the efficiency of baroclinic eddy transfer. A number of laboratory and numerical experiments are then inspected a nd carried out to seek confirmation of these parameter dependencies an d obtain quantitative estimates of the constants. It is found that gam ma = 3.9 +/- 0.9 and beta = 12 +/- 3. Finally, the implications of our study to the understanding of integral properties of deep and interme diate convection in the ocean are discussed.