Chaos in a simple model of the three-dimensional, salt-dominated ocean circulation

A simple moments model used in studying the large-scale thermally driven ocean circulation, in one hemisphere, is extended with a set of evolution equations for the basin-averaged salinity gradients. Natural formulations of the boundary conditions for the heat flux and the (virtual) salt flux are given, the latter based on the SST-evaporation feedback. Stommel's box model result, a coexisting thermal and saline solution, is retrieved in the limit of no rotation. Including rotation in a salt-dominated setting, a steady circulation is found which bifurcates for higher Rayleigh numbers in a periodic solution which becomes chaotic through a cascade of subharmonic bifurcations. Periodic motion results from two different mechanisms. First, the stable stationary state bifurcates into a periodic solution where anomalously saline water is advected by the overturning circulation. Second, this periodic solution 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 cycle, by rapid advection and restratification of the entire basin. The basin-averaged vertical density field is stably stratified in the steady and the periodic regimes and remains statically stable in the chaotic regime.