A Simple Global Model for the General Circulation of the Atmosphere

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 [5] and our previous article [29]) 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, in J. Pedlosky [33]. In a less mathematically rigorous way, H. Lamb [21] observed that the only globally valid geostrophic flow that maintains a slow time scale is zonally symmetric (see the comments in N. Phillips [35] and an explicit derivation in H. Jeffreys [19]). c © 1997 John Wiley & Sons, Inc. Communications on Pure and Applied Mathematics, Vol. L, 0707–0752 (1997) c © 1997 John Wiley & Sons, Inc. CCC 0010–3640/97/070707-46 708 J.-L. LIONS, R. TEMAM, AND S. WANG