Encyclopedia of Geodesy

Living Edition
| Editors: Erik Grafarend

Modeling Oceanic Flow: From Global Navier–Stokes to Local Geostrophic Wavelet Modeling

  • Willi Freeden
  • Christian Gerhards
  • Helga Nutz
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02370-0_127-1


Geostrophic flow

A current in the ocean in which the Coriolis force and the pressure gradient are in balance.

Navier–Stokes equations

Differential equations which describe the motion of viscous fluid substances.

Mathematical Modeling of Ocean Flow

Ocean flow has a great influence on mass transport and heat exchange. By modeling oceanic currents, we therefore gain, for instance, a better understanding of weather and climate. In what follows, we devote our attention to the geostrophic oceanic circulation on bounded regions. In a first approximation, the oceanic surfaces under consideration may be assumed to be parts of the boundary of a spherical Earth model. We calculate the oceanic flow under the simplifying assumptions of stationarity, spherically reflected horizontal velocity, and strict neglect of inner frictions. This leads us to large-scale currents, which still give meaningful results for inner oceanic areas as, for example, when applied to the phenomenon of El Niño...


Geoidal Height Mean Dynamic Topography Vectorial Isotropy Geostrophic Flow Spherical Harmonic Modeling 
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.
This is a preview of subscription content, log in to check access.

References and Reading

  1. Albertella, A., Savcenko, R., Bosch, W., and Rummel, R., 2008. Dynamic ocean topography – the geodetic approach. Schriftenreihe des Instituts für Astronomische und Physikalische Geodäsie und der Forschungseinrichtung Satelliten geodäsie, 27, TU München.Google Scholar
  2. Ansorge, R., and Sonar, T., 2009. Mathematical Models of Fluid Dynamics. Weinheim: Wiley.CrossRefGoogle Scholar
  3. Fehlinger, T., Freeden, W., Gramsch, S., Mayer, C., Michel, D., and Schreiner, M., 2007. Local modelling of sea surface topography from (geostrophic) ocean flow. ZAMM, 87, 775–791.CrossRefGoogle Scholar
  4. Freeden, W., 2015. Geomathematics: its role, its aim, and its potential. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd edn. 3–78. Heidelberg: Springer.Google Scholar
  5. Freeden, W., and Gerhards, C., 2012. Geomathematically Oriented Potential Theory. Boca Raton: Chapman & Hall/CRC Press.CrossRefGoogle Scholar
  6. Freeden, W., and Schreiner, M., 2009. Spherical Functions of Mathematical Geosciences – A Scalar, Vectorial and Tensorial Setup. Berlin/Heidelberg: Springer.Google Scholar
  7. Freeden, W., Gervens, T., and Schreiner, M., 1998. Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford: Oxford Science Publications/Clarendon Press.Google Scholar
  8. Freeden, W., Michel, D., and Michel, V., 2005. Local multiscale approximation of geostrophic oceanic flow: theoretical background and aspects of scientific computing. Marine Geodesy, 28, 313–329.CrossRefGoogle Scholar
  9. Maximenko, N., Niiler, P., Rio, M.-H., Melnichenko, O., Centurioni, L., Chambers, D., Zlotnicki, V., and Galperin, B., 2009. Mean dynamic topography of the ocean derived from satellite and drifting buoy data using three different techniques. Journal of Atmospheric and Oceanic Technology, 26, 1910–1919.CrossRefGoogle Scholar
  10. Moritz, H., 2015. Classical physical geodesy. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd ed., 253–290. Heidelberg: Springer.Google Scholar
  11. Nerem, R. S., and Koblinski, C. J., 1994. The geoid and ocean circulation. In Vaníček, P., and Christou, N. T. (eds.), Geoid and its Geophysical Interpretations. Boca Raton: CRC Press.Google Scholar
  12. Pedlosky, J., 1979. Geophysical Fluid Dynamics. New York/Heidelberg/Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Computational Science CenterUniversity of ViennaViennaAustria