Multiple thermohaline states due to variable diffusivity in a hierarchy of simple models

The effect of variable vertical diffusivity is investigated in dynamically reduced models of the thermohaline circulation (THC) in a rectangular basin. In a simple box model, sufficiently strong variation of the diffusivity κ_v with stability G can lead to the existence of two stable equilibria. Related behaviour is found in well-resolved frictional geostrophic (FG) models. A hierarchy of under-resolved FG models is constructed, the simplest of which is an 8-cell cube, to connect the two extremes of resolution. Multiple solutions in low-order models are found to correspond to the formation of high-gradient layers which are unlikely to be resolved by current ocean models. Physical arguments show that layering and multiple solutions require κ_v to decrease more rapidly than 1/G and sensitivity experiments suggest that, in addition, κ_v must vary by a factor of 10–100. In two-hemisphere runs with salinity forcing included, the dependence of diffusivity on stratification is found to marginally favour equatorially symmetric states. Finally, such variation is shown to have a profound effect on the periodic, flush-collapse cycle under strong saline forcing; specifically, if diffusivity is taken to be a function of stratification rather than depth, regime transitions can occur much more easily. It will therefore be important for climate modelling to determine which is more realistic.