A Simple Model of Millennial Oscillations of the Thermohaline Circulation

Abstract

Abstract Stommel’s two-box model of thermohaline circulation is modified to include the possibility of convection. When reduced to a two-degrees-of-freedom dynamical system, the model exhibits the well-known multiple (thermal and haline) steady states as well as new convective thermal steady states. However, for some values of the control parameters (such as the freshwater flux) oscillations occur. Millennial period oscillatory regimes correspond to switches between the Stommel’s haline fixed point and the convective thermal state, both of which are unstable in a window of precipitation values. The transitions between steady and oscillatory regimes at the boundaries of the window are global bifurcations, which in some cases have an infinite period character. This character is due either to the proximity of the Stommel saddle node bifurcation or to the infinite time it takes for the convection to resume when the system is in the haline regime. The oscillations bear a close relationship to those of Welander’s flip–flop model. The physics of this class of millennial oscillations may be relevant to those observed in more complex OGCMs and may help to rationalize certain features of the millennial band oscillations that punctuate the last glacial period.