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Abstract
Recent studies of the planetary waves in the atmosphere have suggested that the vorticity equation assumes a quasi-stationary character for motions whose scale is comparable to the radius of the earth. These tentative results are adopted as a working hypothesis, and a preliminary study is made of the stability and structure of the waves which are possible in an atmospheric model which is formulated on the basis of the working hypothesis.
It is shown that the assumed stationary form of the vorticity equation acts as a filter which eliminates the Rossby type waves from the solution of the linearized equations in the two-parameter case. The wave-solutions in a linearized form of a three-parameter model are next found and investigated. The major results are that only slowly moving waves are possible and that unstable wave-solutions will appear for sufficiently large vertical wind-shears. A modified form of the model in which horizontal advection of vorticity is also included is analyzed, and it is shown that a wave-length of maximum instability occurs.
A prediction model which can be used in studies of the planetary waves is formulated. Since the model will apply to planetary scales only, it can be used to study the importance of non-linear interactions between the planetary scales and smaller scales.
