Bifurcation Structure of Thermohaline Millennial Oscillations

Abstract

Abstract The question of the generation of millennial oscillations by internal ocean dynamics is studied through deliberate use of the simplest geometry and surface forcing, namely a hemispheric ocean with time-independent mixed boundary conditions (autonomous system). The lowest-order model that supports free oscillations has three horizontal and two vertical boxes. The essential ingredients permitting the existence of the oscillations are turbulent mixing and freshwater forcing. The finite amplitude oscillations share the advective–convective–diffusive characteristics of neighboring stable thermal and haline steady states. There are limits to the quantity of precipitation in polar regions for the existence of oscillatory states. When the freshwater forcing amplitude is increased, the system evolves from a stable thermal state through a global bifurcation to a finite amplitude limit cycle. The period of the limit cycle remains constant when freshwater is increased until at a second global bifurcation it becomes infinite with a logarithmic behavior characteristic of a homoclinic bifurcation. For still higher values of freshwater, the system locks into the stable haline steady state. These results are confirmed through the use of a two-dimensional latitude–depth model. A sensitivity study carried out with the latter shows that the period (away from the logarithmic singularity) varies as (vertical mixing)−1/3. The implications of these results for the Dansgaard–Oeschger oscillations of the last glacial period are threefold: First, internal ocean dynamics in a salt-conserving ocean basin and with time-independent boundary conditions are sufficient to allow free transitions between a strong thermal and a weak haline circulation regime provided that the precipitation in polar oceans does not exceed a certain threshold. It is noteworthy that the snow accumulation rates of the last glacial period were about a fourth of Holocene values. Second, the period of the oscillatory state is determined internally, a possible alternative to studies that require external periodic forcing. The range of the periods when estimated with present determinations of oceanic mixing easily accommodates the observations. Third, if the abrupt warming that signals the beginning of a Dansgaard–Oeschger event is interpreted through the present modeling results, its cause is linked to the efficiency of mixing to accumulate heat for a considerable amount of time in the deep ocean when the thermohaline circulation is weak.