Abstract
We analyze the stability of an idealized model of the Atlantic meridional overturning circulation by adopting a two-dimensional Boussinesq model. We define a two-dimensional parameter space descriptive of the freshwater forcing of the system and determine a bounded region on which multiple equilibria are realized. We also analyze the dependence of the response of the system to finite amplitude perturbations in the boundary conditions with different rates of change. It is possible to define a robust separation between slow and fast regimes of forcing. The critical rate of increase is similar to the ratio of the typical intensity of the hydrological cycle to the advective time scale of the system. If the change of the forcing is faster (slower) than the critical rate, the system responds as to instantaneous (adiabatic) changes of the same amplitude. Since the advective time scale is proportional to the square root of the vertical diffusivity, our analysis supports the conjecture that the efficiency of vertical mixing might be critical in determining the response of the ocean circulation to transient climatic changes.
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Lucarini, V., Calmanti, S. & Artale, V. Experimental mathematics: Dependence of the stability properties of a two-dimensional model of the Atlantic ocean circulation on the boundary conditions. Russ. J. Math. Phys. 14, 224–231 (2007). https://doi.org/10.1134/S1061920807020124
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DOI: https://doi.org/10.1134/S1061920807020124