On the structure of transient atmospheric waves Part II

A. WIIN NIELSEN

Abstract

In this second part of a continuing study of the relative structure of transient baroclinic waves an analysis of the behavior of waves in a three-level, quasi-nondivergent model is presented. The procedures applied in the analysis are a straightforward expansion of those used in Part I in which the two-level model was used. The increased algebraic work required by the three level case is eased somewhat by working in the complex domain with respect to the relative amplitudes and phases, but otherwise the methodology is maintained. However, the use of the complex domain makes it possible to obtain the steady states as the roots to cubic equations where complex roots indicate sloping waves. In addition, the stability analysis of the derived steady states goes easier in the new procedure. In view of the discovery of these advantages it was considered worthwhile to reconsider the two-level case where it is possible to solve the time-dependent problem in a closed form (section 2). Section 3 contains the analysis of the three-level case permitting not only vertical changes of the static stability but also deviations from a linear windprofile. While the results in the case of a straight windprofile are a natural extension of the two-level case, it is found that increasing negative windshears in the upper layer will destabilize the steady state solutions.

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