In Stommel's lateral model, two stable steady states exist. One steady state with fast thermohaline circulation, which is driven by cooling/heating, resembles the present-day thermohaline circulation. Another state of slow thermohaline circulation also exists due to evaporation/precipitation. A second thermally-driven steady state, with intermediate thermohaline circulation, is unstable. An oscillatory state oscillating between the baove two steady states has been found in numerical models of thermohaline circulation by other people. This oscillation does not exist in this model.
Stommel (1986) and Welander (1982) found that there is a thermohaline oscillation in their vertical models with turbulent mixing. We show that the existence of this oscillation depends on the rate of change of turbulent diffusivity with respect to density difference between the upper and the lower layer. The common functional forms of turbulent diffusivity postulated for stratified turbulent waters do not allow such thermohaline oscillation.
The vertical model with salt finger mixing shows no thermohaline oscillation under the appropriate flux law. Two steady states exist. The first, due to the variation of the flux ratio, is unstable, and the second is stable. When the evaporation is too large, there is no steady state and the upper layer overturns with the lower layer.