A diffusive box model, consistent with geostrophy, is proposed as an alternative to more usual advective box models of the ocean thermohaline circulation. When vertical diffusion coefficients for T and S are taken as identically equal (the normal assumption in all numerical ocean models to date), the diffusive box model exhibits both steady-state modes and time-dependent behaviors which are essentially indistinguishable from those of an advective model, under both fixed flux and mixed (T restoring) boundary conditions. The thermohaline “circulation” of the diffusive box model, however, is a combination of a convective branch and a vertical diffusive branch, involving zero volume flux. Modifications in behavior of the diffusive box model are investigated for a plausible range of values for the ratio d ≡ Ks/KT of the vertical turbulent diffusivities of S and T. When surface fluxes of heat and freshwater are constant, the model with d ≠ 1 exhibits additional steady-state modes in which convection is absent from the system, as well as a periodic oscillatory mode. Compared to results with d ≡ 1 under mixed surface boundary conditions, the model with d ≠ 1 exhibits extended ranges of multiple equilibria, a different mode transition near present-day values of freshwater forcing magnitude, and the possibility of quasi-periodic oscillatory states. The sensitivity of the present box model, coupled with that previously observed in a primitive equation model (Gargett and Holloway, 1992), raises serious questions about the ability of numerical models to predict the evolution of the ocean thermohaline circulation under changing atmospheric forcing, even if other problems with such prediction were resolved.
Gargett, Ann E., and Bruno Ferron. 1996. "The effects of differential vertical diffusion of T and S in a box model of thermohaline circulation." Journal of Marine Research 54, (5). https://elischolar.library.yale.edu/journal_of_marine_research/2202