Instability of planetary waves and zonal flows in two‐layer models on a sphere

A study is made of the stability of finite amplitude planetary waves by themselves and together with zonal flows in two‐layer quasi‐geostrophic models on a sphere. Critical amplitudes for incipient instability of baroclinic waves, growth rates, perturbation streamfunctions and momentum fluxes are obtained and are compared with the corresponding properties for barotropic waves in the nondivergent barotropic model. The change in the growth rates, perturbation streamfunctions, momentum and heat fluxes due to the superposition of basic planetary waves on zonal flow profiles is examined in two‐layer quasi‐geostrophic models. The presence of the long planetary waves is found to produce regions of preferential development of cyclones and anticyclones. The position of the most intense development, downstream from the long wave troughs or ridges depending on the basic flow profile, is shown to be related to Phillips's criterion for incipient instability. It is also found that the largest of all the growth rates is increased in the presence of baroclinic waves but decreased in the presence of barotropic waves and it is concluded that baroclinic instability, rather than barotropic instability, is the most important factor in the unpredictability of largescale atmospheric motions. Barotropic waves, however, produce larger changes in the disturbance stream‐functions, momentum and heat fluxes; in particular, when superimposed on solid body rotation zonal flow profiles, they may produce zonally averaged perturbation momentum fluxes with both poleward and equatorward components. The presence of planetary waves in the basic profile removes the short wave instability cutoff characteristic of two‐layer quasi‐geostrophic models with purely zonal flow basic profiles.