Abstract
The leading-order equations governing the unsteady dynamics of large-scale atmospheric motions are derived, via a systematic asymptotic approach based on the thin-shell approximation applied to the ellipsoidal model of the Earth’s geoid. We present some solutions of this single set of equations that capture properties of specific atmospheric flows, using field data to choose models for the heat sources that drive the motion. In particular, we describe standing-waves solutions, waves propagating towards the Equator, equatorially trapped waves and we discuss the African Easterly Jet/Waves. This work aims to show the benefits of a systematic analysis based on the governing equations of fluid dynamics.
Highlights
Waves play a fundamental role in the development and evolution of our atmosphere; it is generally accepted, for example, that Rossby waves are the most important large-scale waves, gravity waves and Kelvin waves are significant
Because the oblateness is only slight for the Earth, it is convenient to incorporate this property as a small correction to the otherwise spherical coordinate system; importantly, we show that this contribution to the geometry uncouples from the thermodynamics and dynamics of the atmosphere, at leading order
We invoke an asymptotic method that is driven by the thin-shell approximation, which represents a minimal assumption for the atmosphere enveloping the Earth
Summary
Waves play a fundamental role in the development and evolution of our atmosphere; it is generally accepted, for example, that Rossby waves are the most important large-scale waves (controlling the weather in the midand higher latitudes), gravity (buoyancy) waves and Kelvin waves are significant. We see that any unsteady motion—especially waves—appear at the same order as the underlying dynamic-thermodynamic balance: they do not constitute small perturbations of some uniform (constant) state This is an important and fundamental difference, which, when coupled with the overarching assumption of a thin-shell geometry—the only simplifying assumption we make for the geometry—for the atmosphere over the surface of the Earth, produces a novel approach to these problems. All models that are consistent with physical reality must, be reflections of a common framework because, underlying them all, is just one set of governing equations This fact is a strong motivation to derive a leading-order generic system of (reduced) equations, based on reliable and transparent approximation procedures, as pursued in the present paper. This situation is somewhat similar to that encountered in the investigation of Rossby waves: the beta-plane approximation was the step forward from the f -plane approximation that revealed to Rossby [7] the presence of these waves, but Haurwitz [8] extended the accuracy (especially with regard to the meridional extent of the wave) by taking the spherical shape of the Earth into account (see [9,10])
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