Abstract Open-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.

中文翻译：

---

深对流烟囱的形成和衰变

摘要 在世界海洋的一些局部地点观察到了开阔洋深对流 (DC)，它在上层和深海动力学之间形成了联系。在本文中，我们进一步开发了一个孤立的垂直均质水柱的分析模型，深度可达几公里，通常称为对流烟囱。我们为烟囱在其深化阶段以及随后的重新分层阶段的演变推导出解析解。初始加深阶段被认为主要由海面浮力损失驱动，而最终加深阶段和再分层阶段则受到斜压涡流通过烟囱侧面的浮力传递的影响。对于深化阶段，对于有或没有天气扰动的恒定海面浮力损失，以及海面浮力损失随时间增长的情况，导出了烟囱深度演变的解析解。对于再分层阶段，获得了烟囱半径的时间演变和该阶段持续时间的解析表达式。精确解及其渐近近似与缩放定律和早期作品中报告的模型研究非常一致。理论结果也与格陵兰海烟囱的演化一致，源自 GLORYS 高分辨率海洋再分析。对于一组给定的背景条件，在达到加深阶段的两个特征时间尺度后，可以认为烟囱是成熟的。成熟的烟囱需要更长的时间才能形成，但比过早的烟囱腐烂得更快。烟囱总寿命的最短时间对应于这样一种情况，即在加深阶段的大约一个特征时间尺度上，海面浮力损失突然下降，重新分层阶段开始。