Advertisement

Governing Equations and Approximations

  • Lars Petter RøedEmail author
Chapter
  • 695 Downloads
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)

Abstract

The purpose of this chapter is to familiarize the reader with the equations governing the motion of atmospheres and the oceans. It introduces the well-known Boussinesq and hydrostatic approximations, and outlines the way the shallow water equations and the quasi-geostrophic equations follow from these approximations. The importance of boundary conditions is also emphasized. Readers who are familiar with these equations, approximations, and conditions may skip this chapter without loss of continuity.

Keywords

Shallow Water Equations Hydrostatic Approximation Quasi-geostrophic Equations Potential Vorticity Vertical Turbulent Momentum Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bjerknes V (1904) Das Problem der Vettervorhersage, betrachtet vom Standpunkte der Mechanik und der Physik. Meteor Z 21:1–7Google Scholar
  2. Fofonoff NP (1985) Physical properties of seawater: a new salinity scale and equation of state for seawater. J. Geophys. Res. 90(C2):3332–3342.  https://doi.org/10.1029/JC090iC02p03332
  3. Gill AE (1982) Atmosphere–ocean dynamics. International geophysics series, vol 30. Academic, New YorkGoogle Scholar
  4. Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, Princeton. ISBN 0-691-11892-2Google Scholar
  5. Held IM (2005) The gap between simulation and understanding in climate modelling. Bull Am Meteorol Soc 86:1609–1614CrossRefGoogle Scholar
  6. Lorenz EN (1963) Deterministic non-periodic flow. J Atmos Sci 20:130–141CrossRefGoogle Scholar
  7. McDougall TJ, Feistel R, Pawlowicz R (2013) Thermodynamics of seawater. In: Siedler G, Griffies SM, Gould J, Church JA (eds) Ocean circulation and climate. A 21st century perspective. International geophysics, vol 103. Elsevier, San Diego, pp 141–158.  https://doi.org/10.1016/B978-0-12-391851-2.00006-4
  8. Pedlosky J (1979) Geophysical fluid dynamics. Springer, BerlinCrossRefGoogle Scholar
  9. Stern M (1975) Ocean circulation physics. International geophysics series, vol 19. Academic, New YorkGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeosciencesUniversity of OsloOsloNorway
  2. 2.Norwegian Meteorological InstituteOsloNorway

Personalised recommendations