Abstract
Normal mode solutions are found numerically in a quasi-geostrophic model that includes five or ten vertical levels and either five or nine latitude “levels.” Wind shear and static stability may be adjusted at any of the vertical or latitude levels. Attention is focused on arrangements of static stability and, to a lesser extent, vertical shear that produce large growth rates, while restricting the horizontal gradients of static stability and shear to maintain the validity of the quasi-geostrophic assumption. The association of small static stability and/or large vertical shear in the lower troposphere with large growth rate of short wavelengths found by Staley and Gall is further confirmed. It is also found that rapid amplification of short wavelengths is little diminished even when the small static stability is very localized (in latitude) in the lower troposphere. The perturbations, however, attenuate rapidly away from regions of small static stability. Large static stability above low static stability has only a negligible stabilizing effect. The sign of the slope of a zone of small static stability has no effect on growth rate.
Small static stability on either side of a jet may result in rapidly amplifying short waves with maximum amplitude in the flanks of the jet and small amplitude at the jet core, despite larger baroclinity beneath the jet core.
The ease of obtaining rapid amplification in limited regions of small static stability suggests abundant favorable initial conditions for explosive cyclogenesis. However, the model gives no information on factors contributing to sustained growth.
