Chaos in a simple model of the threedimensional, saltdominated ocean circulation
Abstract
A simple moments model used in studying the largescale thermally driven ocean circulation, in one hemisphere, is extended with a set of evolution equations for the basinaveraged salinity gradients. Natural formulations of the boundary conditions for the heat flux and the (virtual) salt flux are given, the latter based on the SSTevaporation feedback. Stommel's box model result, a coexisting thermal and saline solution, is retrieved in the limit of no rotation. Including rotation in a saltdominated 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 basinaveraged vertical density field is stably stratified in the steady and the periodic regimes and remains statically stable in the chaotic regime.
 Publication:

Climate Dynamics
 Pub Date:
 1998
 DOI:
 10.1007/s003820050236
 Bibcode:
 1998ClDy...14..489V