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Qualitative Behavior and Nonoscillation of Stommel's Thermohaline Box Model

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  • 1 Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

Stommel's two-box model of thermohaline circulation is generalized to incorporate 1) either mixed or Newtonian thermal and saline boundary conditions; 2) temperature-dependent evaporation, including a simple coupled air-sea model; and 3) a nonlinear flow law for meridional overturning. The authors prove that under steady forcing, the generalized model cannot exhibit self-driven oscillations. If the saline adjustment time is larger than the thermal, then 1) there is one and only one, stable “saline” equilibrium state corresponding to evaporation-driven sinking and 2) “thermal” equilibrium states corresponding to sinking in cooling zones may or may not exist. If they do, they come in pairs, one saddle and one stable node or spiral. A nonlinear “wiggly” flow law may lead to more than one such pair.

Abstract

Stommel's two-box model of thermohaline circulation is generalized to incorporate 1) either mixed or Newtonian thermal and saline boundary conditions; 2) temperature-dependent evaporation, including a simple coupled air-sea model; and 3) a nonlinear flow law for meridional overturning. The authors prove that under steady forcing, the generalized model cannot exhibit self-driven oscillations. If the saline adjustment time is larger than the thermal, then 1) there is one and only one, stable “saline” equilibrium state corresponding to evaporation-driven sinking and 2) “thermal” equilibrium states corresponding to sinking in cooling zones may or may not exist. If they do, they come in pairs, one saddle and one stable node or spiral. A nonlinear “wiggly” flow law may lead to more than one such pair.

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