AbstractOpen-ocean deep convection (DC), forming a link between the upper and the deep ocean dynamics, is observed in a few localized sites of the World Ocean. In the present paper, we further develop an analytical model of isolated vertically homogenized water columns, up to a few kilometers deep, usually referred to as convective chimneys. We derive analytical solutions for evolution of a chimney during its deepening phase, as well as during its subsequent restratification phase. The initial deepening stage is considered to be primarily driven by the buoyancy loss at the sea surface, while the final deepening stage and the restratification phase are affected by a buoyancy transfer through the lateral surface of the chimney by baroclinic eddies.
For the deepening phase, analytical solutions for evolution of the depth of a chimney are derived for a constant sea-surface buoyancy loss with or without synoptic perturbations, and for a case of the sea-surface buoyancy loss growing in time. For the restratification phase, time evolution of the chimney radius and an analytical expression for duration of this phase are obtained. The exact solutions and their asymptotic approximations are in good agreement with the scaling laws and with model studies reported in earlier works. The theoretical results also agree with an evolution of a chimney in the Greenland Sea, derived from GLORYS high-resolution ocean reanalysis.
For a given set of the background conditions, a chimney can be considered a mature one after two characteristic time scales of the deepening phase are reached. A mature chimney needs a longer time for its formation, but decays more rapidly than a pre-mature one. The minimum overall chimney lifetime corresponds to the case, when, at about one characteristic time scale of the deepening phase, the sea-surface buoyancy loss abruptly drops down and the restratification phase begins.