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Quasi-geostrophic equations : ウィキペディア英語版
Quasi-geostrophic equations

While geostrophic motion refers to the wind that would result from an exact balance between the Coriolis force and horizontal pressure gradient forces,〔Phillips, N.A. (1963). “Geostrophic Motion.” Reviews of Geophysics Volume 1, No. 2., p. 123.〕 Quasi-geostrophic (QG) motion refers to flows where the Coriolis force and pressure gradient forces are ''almost'' in balance, but with inertia also having an effect.
〔Kundu, P.K. and Cohen, I.M. (2008). Fluid Mechanics, 4th edition. Elsevier., p. 658.〕
==Origin==
Atmospheric and oceanographic flows take place over horizontal length scales which are very large compared to their vertical length scale, and so they can be described using the shallow water equations. The Rossby number is a dimensionless number which characterises the strength of inertia compared to the strength of the Coriolis force. The quasi-geostrophic equations are approximations to the shallow water equations in the limit of small Rossby number, so that inertial forces are an order of magnitude smaller than the Coriolis and pressure forces. If the Rossby number is equal to zero then we recover geostrophic flow.

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