Derivation of the equations of atmospheric motion in oblate spheroidal coordinates

Since earth is more nearly an oblate spheroid than a sphere, it is of at least theoretical interest to develop the atmospheric equations of motion in spheroidal coordinates. Gates uses the theory of orthogonal curvilinear coordinates, in which the spheroidal equations of relative atmospheric motion...

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Published in:Journal of the atmospheric sciences 2004-10, Vol.61 (20), p.2478-2487
Main Author: GATES, W. Lawrence
Format: Article
Language:English
Subjects:
Atmospheric circulation
Atmospheric models
Earth
Earth, ocean, space
Exact sciences and technology
External geophysics
Kinetic energy
Meteorology
Spheres
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description Since earth is more nearly an oblate spheroid than a sphere, it is of at least theoretical interest to develop the atmospheric equations of motion in spheroidal coordinates. Gates uses the theory of orthogonal curvilinear coordinates, in which the spheroidal equations of relative atmospheric motion are derived from the vector equation of absolute motion. The complete spheroidal equations conserve both absolute angular momentum and total kinetic energy, and in the limit as earth's focal distance or eccentricity approaches zero, and reduced to the familiar spherical equations in both the general and hydrostatic cases.
doi_str_mv 10.1175/1520-0469(2004)061<2478:DOTEOA>2.0.CO;2
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subjects Atmospheric circulation
Atmospheric models
Earth
Earth, ocean, space
Exact sciences and technology
External geophysics
Kinetic energy
Meteorology
Spheres
title Derivation of the equations of atmospheric motion in oblate spheroidal coordinates
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