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A simple global model for the general circulation of the atmosphere. (English) Zbl 0992.86001

Summary: In this article we present a new method of Rossby asymptotics for the equations of the atmosphere similar to the geostrophic asymptotics. We depart from the classical geostrophics [see J. G. Charney and our previous article [Topol. Methods Nonlinear Anal. 4, 253-287 (1994; Zbl 0846.35106)]] by considering an asymptotics valid for the whole atmosphere, not only in midlatitude regions, and by taking into account the spherical form of the Earth. We obtain in this way a very simple global circulation model of the atmosphere for which the equations of motion for wind and temperature are linear evolution equations similar to the linear Stokes equations. Furthermore, the solutions are independent of longitude, and winds travel exactly to the east or to the west.
In this mathematically oriented article, we do not discuss the physical significance of the model that we derive except for observing that this picture coincides in general terms with the classically averaged data obtained by experimental measurements. We also note that different global geostrophic asymptotics (called planetary geostrophic asymptotics) are considered elsewhere in the literature, for example by J. Pedlosky. In a less mathematically rigorous way, H. Lamb observed that the only globally valid geostrophic flow that maintains a slow time scale is zonally symmetric (for an explicit derivation see H. Jeffrey).

MSC:

86A10 Meteorology and atmospheric physics
35Q35 PDEs in connection with fluid mechanics
76B60 Atmospheric waves (MSC2010)
00A71 General theory of mathematical modeling

Citations:

Zbl 0846.35106
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