Abstract
We study the long-time behavior of the planetary motions of the atmosphere by adopting a formal asymptotic approach based on different time scales. It is hypothesized that effects of uncontrolled and unique inputs of energy in the atmosphere give rise to non-uniform planetary waves which vary slowly in space and time. A simple example of a simplified physical model possessing the essential properties of large-scale atmospheric motions is investigated by generalizing the concept of a discrete resonating system to a system consisting of non-uniform wave trains whose amplitudes are slowly varying functions of time as well as of space. The possibility that the side-band resonances in planetary waves are important is investigated. Equations are derived describing the long-time behavior of a resonantly interacting Rossby wave packet and a zonal flow with weak shear. It is shown that the side-band resonance can cause energy to be gained or lost by the zonal flow; in fact, the potential vorticity of the zonal flow is excited on a longer time scale by planetary waves propagating from other regions of the atmosphere.
This analysis offers a plausible explanation of the generation of zonal atmospheric motion by the planetary wave-weak zonal flow interaction, with the group velocity playing a dominant role in the phenomenon.
