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Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions

Published online by Cambridge University Press:  26 April 2006

Charles Quon  and
Michael Ghil
Charles Quon
Affiliation:
Climate Dynamics Center and Department of Atmospheric Sciences, University of California, Los Angeles, CA 90024-1565, USA Permanent address: Department of Fisheries & Oceans, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada.
Michael Ghil
Affiliation:
Climate Dynamics Center and Department of Atmospheric Sciences, University of California, Los Angeles, CA 90024-1565, USA
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Abstract

Long-term variability in the ocean's thermohaline circulation has attracted considerable attention recently in the context of past and future climate change. Drastic circulation changes are documented in paleoceanographic data and have been simulated by general circulation models of the ocean. The mechanism of spontaneous, abrupt changes in thermohaline circulation is studied here in an idealized context, using a two-dimensional Boussinesq fluid in a rectangular container, over 5 decades of Rayleigh number.

When such a fluid is forced with a specified distribution of temperature and salinity at the surface — symmetric about a vertical axis - it attains a stable two-cell circulation, with the same symmetry. On the other hand, replacement of the specified salinity surface condition with an appropriate symmetric salt-flux condition leads to loss of stability of the symmetric circulation and gives rise to a new, asymmetric state. The extent of asymmetry depends on the magnitude of the thermal Rayleigh number, Ra, and on the strength of the salinity flux, γ. An approximate stability curve in the γ-Ra space, dividing the symmetric from the asymmetric states, is obtained numerically, and the entire range of asymmetric flows, from very slight dominance of one cell to its complete annihilation of the other cell, is explored. The physical mechanism of the pitchfork bifurcation from symmetric to asymmetric states is outlined. The effects of three other parameters of the problem are also discussed, along with implications of our results for glaciation cycles of the geological past and for interdecadal oscillations of the present ocean-atmosphere system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 449 - 483
Copyright
© 1992 Cambridge University Press

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References

Arakawa, A. & Lamb V. 1977 Computational design of the basic dynamical processes of the UCLA general circulation model. Meth. Comput. Phys. 17, 173–265.Google Scholar
Barenblatt G. I. 1979 Similarity, Self-similarity, and Intermediate Asymptotics. New York, London: Publishing Consultants Bureau.
Batchelor G. K. 1954 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. Appl. Maths 12, 209–233.Google Scholar
Boyle, E. A. & Keigwin L. 1987 North Atlantic thermohaline circulation during the past 20,000 years linked to high-latitude surface temperature. Nature 330, 35–40.Google Scholar
Broecker, W. S. & Denton G. H. 1989 The role of ocean-atmosphere reorganizations in glacial cycles. Geochim. Cosmochim Acta 53, 2465–2501.Google Scholar
Broecker W. S., Peteet, D. M. & Rind D. 1985 Does the ocean-atmosphere system have more than one stable mode of operation? Nature 315, 21–25.Google Scholar
Busse F. 1978 Nonlinear properties of thermal convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Bryan F. 1986 High-latitude salinity effects and interhemispheric thermohaline circulation. Nature 323, 301–304.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier-Stokes equations. Maths Comput. 22, 745–762.
Chorin A. J. 1969 On the convergence of discrete approximations to the Navier-Stokes equations. Maths Comput. 23, 341–353.Google Scholar
Daniels, P. G. & Stewartson K. 1977 On the spatial oscillations of a horizontally heated rotating fluid. Math. Proc. Camb. Phil. Soc. 81, 325–349.Google Scholar
Daniels, P. G. & Stewartson K. 1978 On the spatial oscillations of a horizontally heated rotating fluid II. Q. J. Mech. Appl. Maths 31, 113–135.Google Scholar
Defant A. 1961 Physical Oceanography, vol. 1. Pergamon.
Duplessy, J.-C. & Shackleton N. J. 1985 Response of global deep-water circulation to Earth's climatic change 135,000–107,000 years ago. Nature 316, 500–507.Google Scholar
Duplessy J.-C., Shackleton N. J., Fairbanks R. G., Labeyrie L., Oppo, D. & Kallel N. 1988 Deepwater source variations during the last climatic cycle and their impact on the global deepwater circulation. Paleoceanography 3, 343–360.Google Scholar
Fuglister F. C. 1960 Atlantic Ocean atlas of temperature and salinity profiles and data from the International Geophysical Year of 1957–1958. Woods Hole Oceanographic Institution, MA, USA. 209 pp.
Ghil, M. & Childress S. 1987 Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics. Springer. 485 pp.
Ghil M., Mullhaupt, A. & Pestiaux P. 1987 Deep water formation and Quaternary glaciations. Climate dyn. 2, 1–10.Google Scholar
Ghil, M. & Vautard R. 1991 Interdecadal oscillations and the warming trend in global temperature time series. Nature 350, 324–327.Google Scholar
Gill A. E. 1966 The boundary layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515–536.Google Scholar
Guckenheimer, J. & Holmes P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer. 453 pp.
Kagan, B. A. & Maslova N. B. 1990 Multiple equilibria of the thermohaline circulation in a ventilated ocean model. Ocean Modelling, issue 90. (Unpublished manuscript obtainable from: Hooke Institute, Oxford University.)
Kennett, J. P. & Stott L. D. 1990 Proteus and Proto-Oceanus: ancestral Paleogene oceans as revealed from antarctic stable isotopic results ODP LEG 113. Proceedings of the Ocean Drilling Program. Scientific Results, vol. 113, pp. 865–880.Google Scholar
Kennett, R. P. & Stott L. D. 1991 Abrupt deep-sea warming, palaeoceanographic changes and benthic extinctions at the end of the palaeocene. Nature 353, 225–229.Google Scholar
Krishnamurti R. 1973 Some further studies on transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Lohmann G. P. 1978 Response of deep sea to ice ages. Oceanus 21, 58–64.Google Scholar
McIntyre M. E. 1968 The axisymmetric convective regime for a rigidly bounded rotating annulus. J. Fluid Mech. 32, 625–655.Google Scholar
Maier-Reimer, E. & Mikolajewicz 1989 Experiments with an OGCM on the cause of the Younger Dryas. Oceanography 87–100, (ed. A. Ayala-Castanares, W. Wooester, A. Yanez-Arancibia).
Manabe, S. & Stouffer R. J. 1988 Two stable equilibria of a coupled ocean atmosphere model. J. Climate 1, 841–866.Google Scholar
Marotzke, J., Welander, P. & Willebrand, J. 1988 Instability and multiple steady states in a meridional-plan model of the thermohaline circulation. Tellus 40A, 162–149.
Quon C. 1972 High Rayleigh number convection in an enclosure-a numerical study. Phys. Fluids 15, 12–19.Google Scholar
Quon C. 1976 A mixed spectral and finite difference model to study baroclinic annulus waves. J. Comput. Phys. 29, 442–479.Google Scholar
Quon C. 1980 Quasi-steady symmetric regimes of a rotating annulus differentially heated on the horizontal boundaries. J. Atmos. Sci. 37, 2407–2423.Google Scholar
Quon C. 1983 Effect of grid distribution on the computation of high Rayleigh number convection in a differentially heated cavity. In Numerical Properties and Methodologies in Heat Transfer (ed. T. M. Shih), pp. 261–281. Hemisphere and Springer.
Quon C. 1987 Nonlinear response of a rotating fluid to differential heating from below. J. Fluid Mech. 181, 233–263.Google Scholar
Rooth C. 1982 Hydrology and ocean circulation. Prog. Oceanogr. 11, 131–149.Google Scholar
Schnitker D. 1982 Climatic variability and deep ocean circulation: evidence from the Northern Atlantic Paleogeogr. 40, 213–234.Google Scholar
Shackleton N. J., Duplessy J.-C., Arnold M., Maurice P., Hall, M. A. & Cartlidge J. 1988 Radiocarbon age of last glacial Pacific deep water. Nature 335, 708–710.Google Scholar
Stommel H. M. 1961 Thermohaline convection with two stable regimes of flow Tellus XIII 2, 224–230.Google Scholar
Thual, O. & McWilliams J. C. 1992 The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box model. J. Geophys. Astrophys. Fluid Dyn. 64, 67–95.Google Scholar
Turner J. S. 1973 Buoyancy Effects on Fluids. Cambridge University Press.
Varga R. S. 1962 Matrix Iterative Analysis. Prentice-Hall.
Weaver, A. J. & Sarachik E. S. 1991 The role of mixed boundary conditions in numerical models of the ocean's climate. J. Phys. Oceanogr. 21, 1470–1493.Google Scholar
Welander P. 1986 Thermohaline effects in the ocean circulation and related simple models. In Large-scale Transport Processes in Oceans and Atmosphere (ed. J. Willebrand & D. T. L. Anderson), pp. 163–200. D. Reidel.
Weyl P. K. 1968 The role of the oceans in climatic change: A theory of the ice ages. Meteorol. Monogr. 8 (30), 37–62.Google Scholar
Wright, D. G. & Stocker T. F. 1991 A zonally averaged ocean model for the thermohaline circulation. Part I: Model development and flow dynamics. J. Phys. Oceanogr. 21, 1713–1724.Google Scholar