A theoretical study of three-dimensional barotropic instability with applications to the upper stratosphere
A numerical method for tropospheric baroclinic instability is used to establish the structures, phase speeds and growth rates of the normal modes of a number of idealized barotropically unstable mean zonal wind fields in a quasi-geostrophic Boussinesq framework. The objective was to gain insight into the effects of vertical mean flow variation on barotropically unstable stratosphere. Both horizontally symmetric and asymmetric flows are considered, but in all cases the flows are vertically symmetric. Major findings show that (1) the wave growth rates associated with the strongest expected horizontal shears decrease with increasing vertical shear and are at least 28% smaller for the weakest expected vertical shear than with no shear; (2) differences in the form of either the vertical or the horizontal shear flow can affect this growth rate reduction by about 25%; and (3) the vertical scale of the barotropic unstable waves is of the order of the geometric mean of the vertical mean flow scale and the vertical penetrat