Abstract
We derive, from the general, governing equations for a viscous, compressible fluid, a generic system of equations that describe the dynamics of the steady atmosphere. This formulation uses suitable rotating coordinates based on an ellipsoidal model for the Earth's geoid and allows for thermodynamic forcing. We invoke only the thin-shell approximation and the geometrical approximation (nearly spherical), retaining all other parameters. Thus we present a general theory for atmospheric flows, based on well-defined approximation methods. This leads to a perturbation of the stationary background state which produces a somewhat familiar, general structure, but with a forcing that is generated by a suitable form of the perturbation temperature field. We show how the new system recovers the classical Ekman, geostrophic and thermal-wind models, expressed more generally in rotating, spheroidal geometry. The new system is also used to present solutions for the Hadley-Ferrel-polar cell structure, for the Walker circulation and to describe the flow in the middle atmosphere. In all these examples, our approach enables us to describe in detail the velocity field and to show how it is possible to identify the heat sources required to maintain the motion.
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