The bifurcation structure of decadal thermohaline oscillations

Abstract

A classification is made for the intrinsic decadal modes of variability in the thermohaline circulation in an oceanic model with steady boundary conditions in a simply-shaped, hemispheric domain with a coarse spatial grid, without the capability of generating any mesoscale eddies. The purpose is to provide an overview of many previous and more specific examples of such variability to better understand its essential characteristics and potential roles in climate change. Various control parameters – including ones expressing the intensities (i.e., Rayleigh numbers) and patterns associated with the surface heat and freshwater forcing – are shown to be important in determining the particular critical values of the thermohaline regime transitions, but they do not modify the overall structure of the bifurcation diagrams. An important categorical distinction is associated with the mathematical form of the surface boundary conditions in determining whether distinguishable decadal variability occurs and, if so, its character. Specified (fixed) patterns for heat and water flux are more permissive of intrinsic decadal variability, and they have a simpler dynamical interpretation for it than do the so-called mixed surface boundary conditions with fixed freshwater flux and thermal relaxation patterns. Both types of boundary conditions are idealizations of the true ocean–atmosphere interactions in climate. The routes to decadal oscillation are quite different for the two types of boundary conditions, namely, a simple Hopf bifurcation for flux conditions and a global bifurcation for mixed conditions. Consequently, with transient forcing distinguishable decadal, variability is evident even for sub-critical parameter values for flux conditions but not for mixed conditions. Furthermore, mixed conditions are more permissive of multiple steady states than are flux conditions.