Advective Time Lags in Box Models

We consider a box model of the thermohaline circulation with mixed boundary conditions in which advective processes are incorporated via an explicit time delay mechanism. The pipes which connect the subtropical and subpolar boxes have a nite volume and do not interact with the atmosphere or with the rest of the ocean except for channeling uxes between the subtropical and subpolar regions. The connguration can be reduced to a two-box model which, unlike the traditional Stommel model, incorporates nite-time advective processes. We nd that including a time lag leaves the haline dominant steady state stable, but the thermally dominant steady state which is stable in Stommel's model can have an oscillatory instability. However, this instability does not lead to sustained oscillations. Instead, it simply makes the circulation cross over to the stable haline dominant pattern. Even in part of the parameter range for which the thermally dominant state remains linearly stable, the time lag leads to a nite-amplitude instability, so that a relatively small { but not innnitesimal { perturbation about the thermal state can switch the circulation to the haline state. 1. Introduction Climate variability on time scales of the order of a decade or longer is a central issue in climate dynamics (for reviews, see 1] 2] 3] and 4]). While this variability is not well understood, there is consensus among many ocean dynamicists that the thermohaline circulation plays a role in it (but see 2] 3] for opinions to the contrary). Models of the thermohaline circulation, of varying degrees of complexity , exhibit a multiplicity of solutions corresponding to diierent climatic states; they may also possess unsteady behavior in the form of oscillatory and temporally irregular solutions. Large-scale oceanic