On the structure of transient atmospheric waves. Part III



In the third and final paper in the series on the relative structure of transient atmospheric waves we consider a model atmosphere with a continuous specification of the zonal wind and the static stability in the basic state. The vertical variations of the parameters in the basic state (except the stability) and in the perturbations will be represented as series expansions in functions appropriate to the vertical variation of the static stability parameter. For the stability we shall consider two cases. The first is a constant static stability in the whole model, and the second is a case where the stability varies as inversely proportional to the square of the pressure. In the first case we may use trigonometric functions to describe the vertical variation. In the second case we derive the appropriate structure functions in the paper, but it turns out that to satisfy the upper boundary condition it is necessary to assume that the top of the atmosphere is located at a pressure larger than zero. The relative structure is in each case obtained as a solution to the stationary equations for the relative amplitude and the relative phase angle. Such solutions are in simple cases obtained directly, but in more complicated cases by numerical integrations carried out to a point where an asymptotic steady state is obtained.

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