Oceans and Atmospheres

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 36)


Chapter 3 deals with a selection of phenomena in classical GFD. The first part of the chapter is largely bound up with the derivation of the quasi-geostrophic potential vorticity equation in the troposphere, following Pedlosky’s derivation, but in addition providing a self-consistent recipe for the determination of the stratification parameter. The interesting possibility of atmospheric overturn arises as a consequence. The chapter concludes with discussion of some oceanic topics, in particular western boundary currents and the tides.


Gravity Wave Rossby Wave Planetary Boundary Layer Short Wave Radiation Thermal Boundary Condition 
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  1. Abramowitz M, Stegun I (1964) Handbook of mathematical functions. Dover, New York MATHGoogle Scholar
  2. Andrews DG (2000) An introduction to atmospheric physics. Cambridge University Press, Cambridge Google Scholar
  3. Barry RG, Chorley RJ (1998) Atmosphere, weather and climate, 7th edn. Routledge, London Google Scholar
  4. Broecker WS (1991) The great ocean conveyor. Oceanography 4:79–89 Google Scholar
  5. Colling A (ed) (2001) Ocean circulation, 2nd edn. Butterworth–Heinemann, Oxford Google Scholar
  6. Defant A (1958) Ebb and flow: the tides of Earth, air and water. University of Michigan Press, Ann Arbor Google Scholar
  7. Fowler AC (1997) Mathematical models in the applied sciences. Cambridge University Press, Cambridge Google Scholar
  8. Ghil M, Childress S (1987) Topics in geophysical fluid dynamics. Springer, Berlin MATHGoogle Scholar
  9. Gill AE (1982) Atmosphere-ocean dynamics. Academic Press, San Diego Google Scholar
  10. Holton JR (2004) An introduction to dynamic meteorology, 4th edn. Elsevier, Burlington Google Scholar
  11. Houghton JT (2002) The physics of atmospheres, 3rd edn. Cambridge University Press, Cambridge Google Scholar
  12. Kalnay E (2003) Atmospheric modeling, data assimilation and predictability. Cambridge University Press, Cambridge Google Scholar
  13. Lamb, Sir Horace (1945) Hydrodynamics, 6th edn. Dover reprint of the 1932 sixth edition. Dover, New York Google Scholar
  14. Lynch P (2006) The emergence of numerical weather prediction: Richardson’s dream. Cambridge University Press, Cambridge Google Scholar
  15. Matuszkiewicz A, Flamand JC, Bouré JA (1987) The bubble-slug flow pattern transition and instabilities of void-fraction waves. Int J Multiph Flow 13:199–217 CrossRefGoogle Scholar
  16. Miller RN (2007) Numerical modelling of ocean circulation. Cambridge University Press, Cambridge CrossRefGoogle Scholar
  17. Olbers D (2001) A gallery of simple models from climate physics. Prog Probab 49:3–63 MathSciNetGoogle Scholar
  18. Pedlosky J (1987) Geophysical fluid dynamics, 2nd edn. Springer, Berlin MATHGoogle Scholar
  19. Prosperetti A, Satrape JV (1990) Stability of two-phase flow models. In: Joseph DD, Schaeffer DG (eds) Two-phase flow models and waves. Springer, New York, pp 98–117 Google Scholar
  20. Shapiro MA, Keyser DA (1990) Fronts, jet streams and the tropopause. In: Newton CW, Holopainen EO (eds) Extratropical cyclones. The Erik Palmén memorial volume. Amer Met Soc, Boston, pp 167–191 Google Scholar
  21. Vallis G (2006) Atmospheric and oceanic fluid dynamics. Cambridge University Press, Cambridge CrossRefGoogle Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics & StatisticsUniversity of LimerickLimerickIreland

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