Definition
- Geostrophic flow :
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A current in the ocean in which the Coriolis force and the pressure gradient are in balance.
- Navier–Stokes equations :
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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...
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References and Reading
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.
Ansorge, R., and Sonar, T., 2009. Mathematical Models of Fluid Dynamics. Weinheim: Wiley.
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.
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.
Freeden, W., and Gerhards, C., 2012. Geomathematically Oriented Potential Theory. Boca Raton: Chapman & Hall/CRC Press.
Freeden, W., and Schreiner, M., 2009. Spherical Functions of Mathematical Geosciences – A Scalar, Vectorial and Tensorial Setup. Berlin/Heidelberg: Springer.
Freeden, W., Gervens, T., and Schreiner, M., 1998. Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford: Oxford Science Publications/Clarendon Press.
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.
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.
Moritz, H., 2015. Classical physical geodesy. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd ed., 253–290. Heidelberg: Springer.
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.
Pedlosky, J., 1979. Geophysical Fluid Dynamics. New York/Heidelberg/Berlin: Springer.
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Freeden, W., Gerhards, C., Nutz, H. (2015). Modeling Oceanic Flow: From Global Navier–Stokes to Local Geostrophic Wavelet Modeling. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_127-1
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DOI: https://doi.org/10.1007/978-3-319-02370-0_127-1
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