Baroclinic Instability and the Selection of the Zonal Scale of the Transient Eddies of Middle Latitudes

Abstract

Because the linear growth rates of baroclinic waves on realistic zonal flows are largest at relatively high zonal wavenumbers (e.g., 15), the observed peaks in the transient kinetic energy spectrum cannot be explained simply by peaks in the linear growth-rate spectrum. When the growth-rate spectrum is fairly flat, as suggested by recent studies, then as the waves evolve, the decrease of the instability of the zonal flow and the increase of dissipation in the developing waves become important in determining which wavelength will dominate after the waves are fully developed. In particular, the stabilization of the zonal flow because of northward and upward eddy transport (which is primarily confined to the lower troposphere in all baroclinic waves) causes the instability of the short baroclinic waves (wavenumber > 10) to decrease more rapidly than that of the intermediate-scale waves (wavenumber <10). In addition, as it is usually modeled, dissipation increases with time more rapidly in the short waves. Therefore, the growth of the short waves is terminated by these two processes before the growth of the intermediate-scale waves, which can thus achieve greater equilibrium amplitudes. We have obtained these results in a numerical experiment with a simplified general circulation model, in which waves of all wavelengths are allowed to develop simultaneously from small random perturbations on a flow that is initially zonally symmetric. The kinetic energy spectrum in this experiment does not display a ?3 power law in the wavenumber band 10?20, even after the spectrum in this spectral region has been equilibrated for a simulated week or more. This result apparently supports the recent hypothesis of Andrews and Hoskins that atmospheric fronts rather than quasi-geostrophic turbulence are responsible for the observed ?3 spectrum at wavenumbers > 10.