Analytical Formulas for the Structure of Perturbations in the Eady Model of Baroclinic Instability in the p-System

Shortly after World War II, the first two models of baroclinic instability were independently published by Charney (1947) and Eady (1949). Both authors describe the origin and initial development of midlatitude weather disturbances from infinitesimal perturbations of a certain initial state of the atmosphere. In this paper we focus on the latter model (Eady, 1949). Using the normal mode method, we derive analytical formulas for the structure of perturbations in the field of geopotential, temperature, isobaric divergence, and vertical velocity. We work in the p coordinate system, in contrast to the original Eady study and its modifications. This allows us to not limit ourselves to the troposphere but to introduce a natural boundary condition at the upper boundary of the atmosphere. The derived analytical relationships accurately well describe some aspects of synoptic disturbances in the midlatitudes. We focus particularly on the wavelength of disturbances, their vertical structure, the position of the minimum divergence level, and the growth rate of emerging synoptic disturbances.