Abstract Whitehead’s ‘tank model’ (Whitehead, 2000) describes a localized deep convective site exchanging water with a two-layer neighbouring ocean basin at three vertical levels. We generalize the original model for the case of arbitrary temperatures and salinities of water layers under an assumption of a constant surface heat flux to the atmosphere in the convective area. The generalized model has unique stable steady state for any value of the heat flux. We then explore analytically the regimes with multiple steady states for a temperature-dependent heat flux to the atmosphere. In this latter case, the multiple steady states are possible and the condition for their existence is derived analytically. Depending on the values of the non-dimensional model parameters, the solution allows for a different number of steady states: from zero to three. The Lyapunov stability analysis showed that, in the case of three steady states, only two of them are stable. The model results are tested against the observations in the Greenland Sea. The results show that the model, in spite of its simplicity, adequately describes many basic features of water exchange between the region of a frequent development of deep convection in the Greenland Sea and the surrounding ocean. The model predicts a negligibly small probability for existence of multiple steady states, which might result from a feedback between the horizontal advection and the deep convection in the Greenland Sea.

中文翻译：

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多稳态远洋深对流解析模型

摘要 Whitehead 的“水槽模型”（Whitehead，2000 年）描述了一个局部深对流站点，在三个垂直层与相邻的两层洋盆交换水。我们在假设对流区大气的表面热通量恒定的情况下，将原始模型推广到任意温度和水层盐度的情况。对于任何热通量值，广义模型都具有独特的稳定稳态。然后，我们分析地探索了具有多个稳态的状态，以实现与温度相关的大气热通量。在后一种情况下，多个稳态是可能的，它们存在的条件是通过分析推导出来的。根据无量纲模型参数的值，该解决方案允许不同数量的稳态：从零到三个。李雅普诺夫稳定性分析表明，在三个稳态的情况下，只有两个是稳定的。模型结果与格陵兰海的观测结果进行了对比。结果表明，该模型尽管简单，但充分描述了格陵兰海深对流频繁发展的区域与周围海洋之间水交换的许多基本特征。该模型预测存在多个稳态的可能性微乎其微，这可能是由于格陵兰海水平对流和深对流之间的反馈造成的。尽管它很简单，但它充分描述了格陵兰海深对流频繁发展的区域与周围海洋之间水交换的许多基本特征。该模型预测存在多个稳态的可能性微乎其微，这可能是由于格陵兰海水平对流和深对流之间的反馈造成的。尽管它很简单，但它充分描述了格陵兰海深对流频繁发展的区域与周围海洋之间水交换的许多基本特征。该模型预测存在多个稳态的可能性微乎其微，这可能是由于格陵兰海水平对流和深对流之间的反馈造成的。