Geostrophic adjustment in a stratified atmosphere

Abstract

The geostrophic adjustment process in a compressible atmosphere with arbitrary vertical stratification is studied as an initial value problem. The governing equations are the adiabatic quasi-static equations on an f-plane linearized about a motionless basic state. A rigid lid upper boundary condition is assumed which permits the use of a discrete eigenfunction expansion in the vertical. Using Fourier transforms in the horizontal a general solution is obtained for both the transient and final states. The general solution is evaluated for several simple experiments with axisymmetric initial conditions in the mass and vorticity fields which have horizontal variations on the tropical cloud cluster scale. These experiments assume a basic state characterized by constant static stability in log-pressure coordinates and a Coriolis parameter corresponding to 20°N latitude. Results are presented which illustrate the nature of the transient adjustment process. Comparison of the initial and final states indicates that the inclusion of vertical structure does not alter the basic conclusion from previous barotropic studies that in the tropics the mass field tends to adjust to the wind field. However, it is found that the extent of this adjustment depends strongly on the vertical structure of the initial conditions. These results are interpreted in term s of the projection of the initial conditions onto the vertical modes.