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Motion on a β ‐planet
Author(s) -
Egger Joseph
Publication year - 2010
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.682
Subject(s) - hydrostatic equilibrium , angular momentum , primitive equations , plane (geometry) , physics , classical mechanics , planet , flow (mathematics) , equations of motion , surface (topology) , momentum (technical analysis) , mechanics , simultaneous equations , mathematics , geometry , differential equation , astronomy , finance , quantum mechanics , economics
It is well known that the standard β ‐plane is not a physical object. As a consequence, angular momentum is not conserved by the related flow equations. The flow equations for a β ‐planet with linearly varying Coriolis parameter and for an infinitely extended β ‐tube are derived in order to see whether these shortcomings can be removed while retaining the simplicity of the β ‐plane equations. The equations conserve axial angular momentum, but the β ‐planet offers no simplification with respect to the spherical case. However, the hydrostatic β ‐tube equations are isomorphic to those of the β ‐plane. Thus the standard β ‐plane equations also deal with flows on a physical surface. Copyright © 2010 Royal Meteorological Society