Abstract
In this chapter we take up the study of the dynamics of a shallow, rotating layer of homogeneous incompressible and inviscid fluid. There are two purposes to our consideration of this physical system. It is first of all simple enough so that the issues raised by the problem of geostrophic degeneracy can be dealt with directly without the need to simultaneously treat the complexities of the thermodynamics of a density-stratified fluid. The first goal of the present chapter is to illustrate how the geostrophic approximation can be systematically exploited to produce a deterministic dynamical framework adequate for the calculation of motions of large time and space scales. Furthermore, the method of analysis to be presented also can be generalized to the study of thermodynamically active fluids. The key technique of the analysis is the formulation of a systematic approximation scheme in which the geostrophic approximation is merely the first step.
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Selected Bibliography
Section 3.1
Rossby, C. G., et al. 1939. Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Marine Res. 2, 38–55.
Stommel. H. 1948. The westward intensification of wind-driven ocean currents. Trans. Amer. Geoph. Union 29, 202–206.
Section 3.22
Longuet-Higgins, M. S. 1964. On group velocity and energy flux in planetary wave motions. Deep-Sea Research 11, 35–42.
Section 3.24
Jeffreys, H. A. and Jeffreys, B. S. 1962. Methods of Mathematical Physics. Cambridge University Press.
Rossby, C. G. 1945. On the propagation of frequencies and energy in certain types of oceanic and atmospheric waves. J. Meteor. 2, 187–204.
Section 3.25
Flierl, G. R. 1977. Simple applications of McWilliams’s “A note on a consistent quasi-geostrophic model in a multiply connected domain”. Dynamics of Atmospheres and Oceans 1, 443–454.
Greenspan, H. P. 1968. The Theory of Rotating Fluids. Cambridge University Press, 327 pp.
Longuet-Higgins, M. S. 1964. Planetary waves on a rotating sphere. Proc. Royal Soc. A 279, 446–473.
Pedlosky, J. 1965. A study of the time dependent ocean circulation. J. Atmos. Sci. 22, 267–272.
Section 3.26
Gill, A. E. 1974. The stability of planetary waves on an infinite beta-plane. Geophysical Fluid Dynamics 6, 29–47.
Longuet-Higgins, M. S. and Gill, A. E. 1967. Resonant interactions between planetary waves. Proc. Roy. Soc. A 299, 120–140.
Lorenz, E. N. 1972. Barotropic instability of Rossby wave motion. J. Atmos. Sci. 29, 258–269.
Section 3.27
Charney, J. G. 1971. Geostrophic Turbulence. J. Atmos. Sci. 28, 1087–1095.
Fjortoft, R. 1953. On the changes in the spectral distribution of kinetic energy for a two-dimensional, non-divergent flow. Tellus 5, 225–237.
Rhines, P. B. 1975. Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417–433.
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Pedlosky, J. (1982). Inviscid Shallow-Water Theory. In: Geophysical Fluid Dynamics. Springer study edition. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25730-2_3
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DOI: https://doi.org/10.1007/978-3-662-25730-2_3
Publisher Name: Springer, Berlin, Heidelberg
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