Advective time lags in box models

A box model of the thermohaline circulation with mixed boundary conditions in which advective processes are incorporated via an explicit time delay me chanism is considered. The pipes that connect the subtropical and subpolar boxes have a finite volume and do not interact with the atmosphere or with the rest of the ocean except for channeling fluxes between the subtropical and subpolar regions. The configuration can be reduced to a two-box model, which, unlike the traditional Stommel model, incorporates finite-time advec tive processes. It is found that including a time lag leaves the haline dom inant steady state stable, but the thermally dominant steady state, which i s stable in Stommel's model, can have an oscillatory instability. However, this instability does not lead to sustained oscillations. Instead, it simpl y makes the circulation cross over to the stable haline dominant pattern. E ven in part of the parameter range for which the thermally dominant state r emains linearly stable, the time lag leads to a finite-amplitude instabilit y so that a relatively small-but not infinitesimal-perturbation about the t hermal state can switch the circulation to the haline state.