CHAOS IN A SIMPLE-MODEL OF THE 3-DIMENSIONAL, SALT DOMINATED OCEAN CIRCULATION

A simple moments model used in studying the large-scale thermally driv en ocean circulation, in one hemisphere, is extended with a set of evo lution equations for the basin-averaged salinity gradients. Natural fo rmulations of the boundary conditions for the heat flux and the (virtu al) salt flux are given, the latter based on the SST-evaporation feedb ack. Stommel's box model result, a coexisting thermal and saline solut ion, is retrieved in the limit of no rotation. Including rotation in a salt-dominated setting, a steady circulation is found which bifurcate s for higher Rayleigh numbers in a periodic solution which becomes cha otic through a cascade of subharmonic bifurcations. Periodic motion re sults from two different mechanisms. First, the stable stationary stat e bifurcates into a periodic solution where anomalously saline water i s advected by the overturning circulation. Second, this periodic solut ion bifurcates into a state which is dominated, during the larger part of the cycle, by diffusion and inertia, characterized by a decreasing overturning rate, and, during the subsequent shorter part of the cycl e, by rapid advection and restratification of the entire basin. The ba sin-averaged vertical density field is stably stratified in the steady and the periodic regimes and remains statically stable in the chaotic regime.