Baroclinic instability governed by the modified quasi-geostrophic equations

Results are presented for the baroclinic instability of zonal flows on a β-plane according to the modified quasi-geostrophic equations (which retain a non-Doppler term in the rigid horizontal boundary condition).Numerical techniques, with up to 180 interior levels, are used. In the absence of a β-effect the instability of the longer waves is fairly sensitive to the non-Doppler term, the more so if static compressibility is neglected. A realistic β-effect markedly reduces this sensitivity: the weakly unstable long waves are essentially internal mode phenomena and are consequently little affected by the non-Doppler term. It is confirmed that the stable external mode Rossby waves, where they exist, are radically altered when the term is included.