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ABSTRACT
The mechanism of baroclinic instability in the Eady model is interpreted by explicitly calculating the ageostrophic circulations related to the model's hyperbolic basic functions. It is advantageous to perform the analysis at the midlevel where the model's "barotropic" mode provides the streamfunction and the "baroclinic" mode represents the temperature. These modes interact and instability occurs if the horizontal advection of background potential temperature by the barotropic mode dominates over the vertical one because of the same mode at the midlevel. A rather simple picture of the stable as well as the unstable flow configurations emerges. Other interpretations are discussed briefly.
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1. Introduction
Eady's model of baroclinic instability (Eady 1949) contains the instability process in a pure and elegant form. The model with its linear mean wind profile and two rigid lids is quite simple but there is nevertheless sufficient similarity between the model's unstable modes and baroclinic waves in the atmosphere to make this instability a paradigm for a dynamical atmospheric mechanism of key importance. In turn, many textbooks of dynamical meteorology provide a discussion of this model where the solution to the model equations and the structure of the normal modes are presented (Pedlosky 1986; Holton 1992). There is still the challenge to interpret the model results in terms of basic dynamical principles. A major step in that direction has been made by Davies and Bishop (1994), who see the baroclinic instability process in the Eady model as an example of interlevel interaction. According to Davies and Bishop (1994), the Eady model captures the interaction of two edge waves riding, respectively, on the grathents of potential temperature that are located at the upper and lower rigid boundaries of the flow domain. These authors reformulated the model equations in terms of these interacting edge waves. Thus, Davies and Bishop (1994) provided a simple, dynamically based explanation of the instability process. The purpose of this article is twofold. First, it will be shown that the approach of Davies and Bishop (1994) can be generalized to a wide class of interacting wave modes. Second, these considerations will lead to a system of maximum simplicity, where the interpretation of the baroclinic instability mechanism in the Eady model is straightforward.
2. General...