The Meridional Overturning Circulation (MOC) in the Atlantic Ocean is an important component of the climate system. Knowledge of its stability and variability is essential to understand past and future climate fluctuations. Conventional ocean models are not well-suited to study these issues. In collaboration with Henk Dijkstra, I was involved in the development of an implicit climate model, THCM (Weijer et al., 2003). This model uses concepts from dynamical systems theory and advanced numerical methods to solve steady patterns of the ocean circulation and their linear stability.
For a 5 degree global configuration, I identified the least stable modes that threaten the stability of a decent global overturing circulation. Among the three least stable modes, two oscillatory modes were found, and one real mode. The oscillatory modes could be identified as overturning oscillations, for which temperature and salinity anomalies are advected by the global overturning circulation (Weijer and Dijkstra, 2003).
For an even higher resolution, we computed the classical hysteresis loop of the global overturning circulation with respect to North Atlantic freshwater input; not by time-integration and monitoring quasi-equilibrium behaviour, but through parameter continuation. This allowed us to identify even the unstable branch connecting the conveyor belt circulation and the collapsed state (Dijkstra and Weijer, 2003; Dijkstra and Weijer, 2005).
Before turning to the global problems, I studied the thermohaline circulation in a double hemispheric configuration, with equatorially symmetric surface forcing. In this context, equatorially asymmetric ("pole-to-pole") circulation patterns arise due to non-linear dynamics of the flow, despite symmetric forcing conditions. The question is whether the mechanism of symmetry breaking, as found in two-dimensional models, survives when three-dimensional effects (particularly rotation) are taken into account. An analysis of the energy transfer between the basic state and the most unstable perturbation showed that the mechanism underlying the symmetry breaking pitchfork bifurcation is essentially the same for two- and three-dimensional models of the thermohaline circulation (Weijer and Dijkstra, 2001).
This work was done in collaboration with Henk Dijkstra at the Institute for Marine and Atmospheric Research Utrecht (IMAU).
Stability
of the global ocean circulation: basic bifurcation diagrams
Dijkstra, H. A., and Weijer, W., 2005.
Journal
of Physical Oceanography,
35, 933-948. Abstract
Full
text (pdf)
A
systematic approach to determine thresholds of the ocean's
thermohaline circulation
Dijkstra, H. A., L. te Raa and W.
Weijer, 2004.
Tellus,
56A, 362-370. Abstract
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text (pdf)
Stability
of the global ocean circulation: the connection of equilibria in a
hierarchy of models
Dijkstra, H. A., and W. Weijer, 2003.
Journal of Marine
Research, 61, 725-743.
Abstract
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text (pdf)
Multiple
oscillatory modes of the global ocean circulation
Weijer,
W., and H. A. Dijkstra, 2003.
Journal
of Physical Oceanography,
33, 2197-2213. Abstract
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text (pdf)
A
fully-implicit model of the global ocean circulation
Weijer,
W., H. A. Dijkstra, H. Oksuzoglu, F. W. Wubs and A. C. de Niet,
2003.
Journal of
Computational Physics,
192, 452-470. Abstract
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text (pdf)
Imperfections
of the three-dimensional thermohaline circulation: Hysteresis and
unique-state regimes
Dijkstra, H. A., W. Weijer and J. D.
Neelin, 2003.
Journal
of Physical Oceanography,
33, 2796-2814. Abstract
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text (pdf)
A
bifurcation study of the three-dimensional thermohaline ocean
circulation: the double-hemispheric case
Weijer, W., and
H. A. Dijkstra, 2001.
Journal
of Marine Research, 59,
599-631. Abstract
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text (pdf)