An analytical model of open-ocean deep convection with multiple steady states


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.
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