A Linear Analysis on the Acceleration of Zonal Flow by Baroclinic Instability. Part I. Terrestrial Atmosphere

A mechanism which accelerates the midlatitude zonal-mean wind is investigated by means of linear stability analysis for the wave-zonal flow interaction. Two kinds of models are analyzed: In the first, the basic state consists of an unstable zonal-mean state and a transient planetary wave with a finite amplitude predicted by a theoretical closure assumption based on the geostrophic turbulence model. In the second, the basic state is prescribed by a statistically stationary wave embedded in an unstable zonal-mean state. The stability of these basic states has been computed numerically for the terrestrial atmosphere using a two-layer quasi-geostrophic model in spherical coordinates. The basic state with the transient planetary wave generates a zonal-mean perturbation having monotonic exponential growth, whereas the basic state with a stationary wave generates a zonal-mean perturbation with oscillatory exponential growth. For both instabilities the primary energy source of the growing perturbations is the available potential energy contained in the basic zonal-mean temperature field. Because of the inherent transiency of the basic transient wave, its acceleration of zonal-mean flow is possible only temporarily, over a short time-interval less than a day, and thus the stationary wave in the basic state appears to be more important in changing the zonal-mean wind and temperature fields. The results of the present analysis compare favorably with the observed characteristics of energy conversion from the eddy kinetic to zonal-mean kinetic energies.