A Zonally Averaged Ocean Model for the Thermohaline Circulation. Part I: Model Development and Flow Dynamics

Abstract

A two-dimensional latitude?depth ocean model is developed on the basis of the zonally averaged balance equations of mass, momentum, heat, and salt. Its purpose is to investigate the dynamics and variability of the buoyancy-forced thermohaline circulation. For the time scales of interest an annually averaged model is selected, and the momentum balance is taken to be diagnostic. The east-west pressure gradient, which arises upon zonally averaging the momentum equations, is parameterized in terms of the meridional pressure gradient. The thermohaline circulation is driven by mixed surface boundary conditions, i.e., temperatures are relaxed to prescribed values while the salt flux is held constant. The dynamics of the flow is investigated in hemispheric and global geometries for both short and long time integrations, the latter extending over many thousands of years. As has been noted by previous investigators, it is possible to perturb a steady state such that a diffusively dominated regime results. By considering a simple analytic model for the diffusive state in an ocean with a linear equation of state, it is demonstrated that any steady, diffusive state is unstable. Convective overturning must occur either at low or at high latitudes. In the former case adjustments are minor, whereas high latitude convection can result in a basinwide rearrangement of the water masses. These two different processes are verified in the present model; violent overturning repeats about every 20 000 years. The application of the model as a component of a two-dimensional paleoclimate model is discussed.