Geophysical Fluid Dynamics and Climate Dynamics

  • Tian Ma
  • Shouhong Wang


Our Earth’s atmosphere and oceans are rotating geophysical fluids that are two important components of the planet’s climate system. The atmosphere and the oceans are extremely rich in their organization and complexity, and many phenomena that they exhibit, involving a broad range of temporal and spatial scales (Charney, 1948), cannot be reproduced in the laboratory. An understanding of the complex scientific issues of geophysical fluid dynamics requires the combined efforts of scientists in many fields. The main objective of this chapter is to initiate a study of dynamic transitions and stability of large-scale atmospheric and oceanic circulations, focusing on a few typical sources of climate variability. Such variability, independently and interactively, may play a significant role in past and future climate change.


  1. Battisti, D. S. and A. C. Hirst (1989). Interannual variability in a tropical atmosphere-ocean model. influence of the basic state, ocean geometry and nonlinearity. J. Atmos. Sci. 46, 1687–1712.CrossRefGoogle Scholar
  2. Bjerknes, V. (1904). Das problem von der wettervorhersage, betrachtet vom standpunkt der. mechanik un der physik. Meteor. Z. 21, 1–7.zbMATHGoogle Scholar
  3. Branstator, G. W. (1987). A striking example of the atmosphere’s leading traveling pattern. J. Atmos. Sci. 44, 2310–2323.CrossRefGoogle Scholar
  4. Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability. Dover Publications, Inc.zbMATHGoogle Scholar
  5. Charney, J. (1947). The dynamics of long waves in a baroclinic westerly current. J. Meteorol. 4, 135–163.MathSciNetCrossRefGoogle Scholar
  6. Charney, J. (1948). On the scale of atmospheric motion. Geofys. Publ. 17(2), 1–17.MathSciNetGoogle Scholar
  7. Dijkstra, H. A. (2000). Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Niño. Dordrecht, the Netherlands: Kluwer Academic Publishers.Google Scholar
  8. Dijkstra, H. A. and M. Ghil (2005). Low-frequency variability of the large-scale ocean circulations: a dynamical systems approach. Review of Geophysics 43, 1–38.CrossRefGoogle Scholar
  9. Dijkstra, H. A. and M. J. Molemaker (1997). Symmetry breaking and overturning oscillations in thermohaline-driven flows. J. Fluid Mech. 331, 195–232.zbMATHCrossRefGoogle Scholar
  10. Dijkstra, H. A. and M. J. Molemaker (1999). Imperfections of the North-Atlantic wind-driven ocean circulation: Continental geometry and wind stress shape. J. Mar. Res. 57, 1–28.CrossRefGoogle Scholar
  11. Dijkstra, H. A. and J. D. Neelin (1999). Imperfections of the thermohaline circulation: Multiple equilibria and flux-correction. J. Clim. 12, 1382–1392.CrossRefGoogle Scholar
  12. Dijkstra, H. A. and J. D. Neelin (2000). Imperfections of the thermohaline circulation: Latitudinal asymmetry versus asymmetric freshwater flux. J. Clim. 13, 366–382.CrossRefGoogle Scholar
  13. Drazin, P. and W. Reid (1981). Hydrodynamic Stability. Cambridge University Press.zbMATHGoogle Scholar
  14. Ghil, M. (1976). Climate stability for a sellers-type model. J. Atmos. Sci. 33, 3–20.MathSciNetCrossRefGoogle Scholar
  15. Ghil, M. (2000). Is our climate stable? Bifurcations, transitions and oscillations in climate dynamics, in Science for survival and sustainable development, V. I. Keilis-Borok and M. Sorondo (eds.), Pontifical Academy of Sciences. pp. 163–184.Google Scholar
  16. Ghil, M. and S. Childress (1987). Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics. Springer-Verlag, New York.zbMATHCrossRefGoogle Scholar
  17. Held, I. M. and M. J. Suarez (1974). Simple albedo feedback models of the ice caps. Tellus 26, 613–629.CrossRefGoogle Scholar
  18. Jin, F. F. (1996). Tropical ocean-atmosphere interaction, the pacific cold tongue, and the el nino southern oscillation. Science 274, 76–78.CrossRefGoogle Scholar
  19. Jin, F. F., D. Neelin, and M. Ghil (1996). El niño southern oscillation and the annual cycle: subharmonic frequency locking and aperiodicity. Physica D 98, 442–465.zbMATHCrossRefGoogle Scholar
  20. Kushnir, Y. (1987). Retrograding wintertime low-frequency disturbances over the north pacific ocean. J. Atmos. Sci. 44, 2727–2742.CrossRefGoogle Scholar
  21. Lions, J.-L., R. Temam, and S. Wang (1992a). New formulations of the primitive equations of atmosphere and applications. Nonlinearity 5(2), 237–288.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Lions, J.-L., R. Temam, and S. Wang (1992b). On the equations of the large-scale ocean. Nonlinearity 5(5), 1007–1053.MathSciNetzbMATHCrossRefGoogle Scholar
  23. Lions, J.-L., R. Temam, and S. Wang (1993). Models for the coupled atmosphere and ocean. (CAO I,II). Comput. Mech. Adv. 1(1), 120.Google Scholar
  24. Lorenz, E. N. (1963a). Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.zbMATHCrossRefGoogle Scholar
  25. Lorenz, E. N. (1963b). The mechanics of vacillation. J. Atmos. Sci. 20, 448–464.CrossRefGoogle Scholar
  26. Lorenz, E. N. (1967). The Nature and Theory of the General Circulation of the Atmosphere. World Meteorological Organization, Geneva, Switzerland.Google Scholar
  27. Ma, T. and S. Wang (2004b). Dynamic bifurcation and stability in the Rayleigh-Bénard convection. Commun. Math. Sci. 2(2), 159–183.MathSciNetzbMATHCrossRefGoogle Scholar
  28. Ma, T. and S. Wang (2005b). Bifurcation theory and applications, Volume 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.Google Scholar
  29. Ma, T. and S. Wang (2005d). Geometric theory of incompressible flows with applications to fluid dynamics, Volume 119 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.zbMATHCrossRefGoogle Scholar
  30. Ma, T. and S. Wang (2007a). Rayleigh-Bénard convection: dynamics and structure in the physical space. Commun. Math. Sci. 5(3), 553–574.MathSciNetzbMATHCrossRefGoogle Scholar
  31. Ma, T. and S. Wang (2010b). Dynamic transition theory for thermohaline circulation. Phys. D 239(3-4), 167–189.MathSciNetzbMATHCrossRefGoogle Scholar
  32. Ma, T. and S. Wang (2010c). Tropical atmospheric circulations: dynamic stability and transitions. Discrete Contin. Dyn. Syst. 26(4), 1399–1417.MathSciNetzbMATHGoogle Scholar
  33. Ma, T. and S. Wang (2011b). El Niño southern oscillation as sporadic oscillations between metastable states. Advances in Atmospheric Sciences 28:3, 612–622.MathSciNetCrossRefGoogle Scholar
  34. Malkus, W. V. R. and G. Veronis (1958). Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.MathSciNetzbMATHCrossRefGoogle Scholar
  35. Neelin, J. D. (1990a). A hybrid coupled general circulation model for el niño studies. J. Atmos. Sci. 47, 674–693.CrossRefGoogle Scholar
  36. Neelin, J. D. (1990b). The slow sea surface temperature mode and the fast-wave limit: Analytic theory for tropical interannual oscillations and experiments in a hybrid coupled model. J. Atmos. Sci. 48, 584–606.CrossRefGoogle Scholar
  37. Neelin, J. D., D. S. Battisti, A. C. Hirst, F.-F. Jin, Y. Wakata, T. Yamagata, and S. E. Zebiak (1998). Enso theory. J. Geophys. Res. 103, 14261–14290.CrossRefGoogle Scholar
  38. Pedlosky, J. (1987). Geophysical Fluid Dynamics (second ed.). New-York: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  39. Philander, S. G. and A. Fedorov (2003). Is el niño sporadic or cyclic? Annu. Rev. Earth Planet. Sci. 31, 579–594.CrossRefGoogle Scholar
  40. Phillips, N. A. (1956). The general circulation of the atmosphere: A numerical experiment. Quart J Roy Meteorol Soc 82, 123–164.CrossRefGoogle Scholar
  41. Quon, C. and M. Ghil (1992). Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions. J. Fluid Mech. 245, 449–484.zbMATHCrossRefGoogle Scholar
  42. Quon, C. and M. Ghil (1995). Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio. J. Fluid Mech. 291, 33–56.MathSciNetzbMATHCrossRefGoogle Scholar
  43. Richardson, L. F. (1922). Weather Prediction by Numerical Process. Cambridge University Press.zbMATHGoogle Scholar
  44. Rooth, C. (1982). Hydrology and ocean circulation. Prog. Oceanogr. 11, 131–149.CrossRefGoogle Scholar
  45. Rossby, C.-G. (1926). On the solution of problems of atmospheric motion by means of model experiment. Mon. Wea. Rev. 54, 237–240.CrossRefGoogle Scholar
  46. Salby, M. L. (1996). Fundamentals of Atmospheric Physics. Academic Press.Google Scholar
  47. Samelson, R. M. (2008). Time-periodic flows in geophysical and classical fluid dynamics. in: Handbook of numerical analysis, special volume on computational methods for the ocean and the atmosphere. R. Temam and J. Tribbia, eds. Elsevier, New York. To appear.Google Scholar
  48. Sardeshmukh, P. D., G. P. Compo, and C. Penland (2000). Changes of probability associated with el niño. Journal of Climate, 4268–4286.CrossRefGoogle Scholar
  49. Schneider, E. K., B. P. Kirtman, D. G. DeWitt, A. Rosati, L. Ji, and J. J. Tribbia (2003). Retrospective ENSO forecasts: Sensitivity to atmospheric model and ocean resolution. Monthly Weather Review 131:12, 3038–3060.CrossRefGoogle Scholar
  50. Schopf, P. S. and M. J. Suarez (1987). Vacillations in a coupled ocean-atmosphere model. J. Atmos. Sci. 45, 549–566.CrossRefGoogle Scholar
  51. Stern, M. E. (1960). The “salt fountain” and thermohaline convection. Tellus 12, 172–175.Google Scholar
  52. Stommel, H. (1961). Thermohaline convection with two stable regimes of flow. Tellus 13, 224–230.CrossRefGoogle Scholar
  53. Thual, O. and J. C. McWilliams (1992). The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models. Geophys. Astrophys. Fluid Dyn. 64, 67–95.CrossRefGoogle Scholar
  54. Tziperman, E. (1997). Inherently unstable climate behavior due to weak thermohaline ocean circulation. Nature 386, 592–595.CrossRefGoogle Scholar
  55. Tziperman, E., J. R. Toggweiler, Y. Feliks, and K. Bryan (1994). Instability of the thermohaline circulation with respect to mixed boundary conditions: Is it really a problem for realistic models? J. Phys. Oceanogr. 24, 217–232.CrossRefGoogle Scholar
  56. Veronis, G. (1963). An analysis of wind-driven ocean circulation with a limited Fourier components. J. Atmos. Sci. 20, 577–593.CrossRefGoogle Scholar
  57. Veronis, G. (1966). Wind-driven ocean circulation, part ii: Numerical solution of the nonlinear problem. Deep-Sea Res. 13, 31–55.Google Scholar
  58. von Neumann, J. (1960). Some remarks on the problem of forecasting climatic fluctuations. In R. L. Pfeffer (Ed.), Dynamics of climate, pp. 9–12. Pergamon Press.Google Scholar
  59. Zebiak, S. E. and M. A. Cane (1987). A model el nino southern oscillation. Mon. Wea. Rev. 115, 2262–2278.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tian Ma
    • 1
  • Shouhong Wang
    • 2
  1. 1.Department of MathematicsSichuan UniversitySichuanChina
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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