Adiabatic Perturbation Equations for a Zonal Atmospheric Current

Abstract

By a proper choice of coordinates and variables, a simple and quasi-symmetrical system of differential equations is obtained for the infinitesimal adiabatic perturbations of the most general continuous zonal air-flow. The coordinate surfaces are those of the orthogonal system built up with the isentropic surfaces and the meridians, and the variables are the displacements of the fluid in the directions of the coordinate lines, and the local disturbance of the pressure. From these perturbation equations a differential equation for the pressure disturbance alone is derived in the case of a wave, and it is then shown that this wave equation can be always greatly simplified if account is taken of the order of magnitude of the various parameters. Simplified expressions are also given for the components of the vibration (fluid displacement). More particular equations and formulae are then derived for short-period, middle-period and long-period waves successively, this classification being made according to the value of the orbital frequency compared to the coefficient of hydrostatic stability and Coriolis parameter, and special cases are also considered where the wave equation reduces to one with constant coefficients (elastic, gravitational, Rossby's waves). Finally some incorrect recently published results are discussed.