Baroclinic instability and submesoscale eddy formation in weakly stratified oceans under cooling

Numerical experiments with a three‐dimensional nonhydrostatic model have been performed to investigate baroclinic instability and submesoscale eddy formation in weakly stratified oceans under cooling. Two types of baroclinic instability can exist in a two‐layered ocean where the convectively formed deep mixed layer overlies the weakly stratified lower layer. One rapidly develops in the mixed layer with short wavelengths (shallow mode), and the other occupies the whole ocean depth with long wavelengths (deep mode). When a background flow is deep, the shallow mode develops first, but the deep mode replaces it in several days. In contrast, only the shallow mode is excited in the mixed layer overlying the strongly stratified layer. The linear stability analysis explains these results well. Despite active cooling, subsequently formed eddies restratify the mixed layer and modify water density over the whole depth. When a background flow is shallow, baroclinic instability is confined to the mixed layer and produces a dipole of surface‐intensified cyclonic eddy and middepth‐intensified anticyclonic eddy, both of which are of submesoscale (∼10 km). The anticyclonic eddy consisting of convectively formed but weakly stratified water moves across the front to ventilate the deep layer, where convection does not reach locally. In this way, density modification extends below the mixed layer. Surface cooling as well as baroclinicity enhances restratification of the mixed layer and density modification at depths by activating submesoscale eddy formation. The results can explain the restratification of the deep mixed layer observed during a cooling season and the origins of submesoscale coherent vortices recently detected in polar oceans.