Abstract
The most important geometrical approximation in geophysical fluid dynamics stems from the effective shallowness of the fluid layers relative to global horizontal scales of atmospheric and oceanic flow. In the present chapter we shall study this approximation in the simplest setting of an incompressible inviscid fluid of constant density, with uniform body force (gravitation) acting vertically downwards. The resulting approximate description of motion in a frame which rotates about a vertical axis is usually referred to as rotating shallow-water theory.
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References
Courant and Hilbert (1953), Chapters V and VI.
Gill (1982), Sections 7.1–7.6, 8.2 and 8.3, 10.4 and 10.5, 11.1–11.8.
Greenspan (1968), Sections 2.6 and 2.7.
Landau and Lifschitz (1959), Section 100.
Pedlosky (1979), Sections 3.1–3.11.
Stoker (1957), Sections 2.2–2.4.
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© 1987 Springer Science+Business Media New York
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Ghil, M., Childress, S. (1987). Effects of Shallowness. In: Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics. Applied Mathematical Sciences, vol 60. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1052-8_2
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DOI: https://doi.org/10.1007/978-1-4612-1052-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96475-1
Online ISBN: 978-1-4612-1052-8
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