A bifurcation study of the three-dimensional thermohaline ocean circulation: the double-hemispheric case

Abstract

Within a low-resolution primitive-equation model of the three-dimensional ocean circulation, a bifurcation analysis is performed of double-hemispheric basin flows. Main focus is on the connection between results for steady two-dimensional flows in a non-rotating basin and those for three-dimensional flows in a rotating basin. With the use of continuation methods, branches of steady states are followed in parameter space and their linear stability is monitored. There is a close qualitative similarity between the bifurcation structure of steady-state solutions of the two- and three dimensional flows. In both cases, symmetry-breaking pitchfork bifurcations are central in generating a multiple equilibria structure. The locations of these pitchfork bifurcations in parameter space can be characterized through a zero of the tendency of a particular energy functional. Although balances controlling the steady-state ?ows are quantitatively very di?erent, the zonally averaged patterns of the perturbations associated with symmetry-breaking are remarkably similar for two-dimensional and three-dimensional ?ows, and the energetics of the symmetry-breaking mechanism is in essence the same.