On the β$$ \beta $$‐effect in the baroclinic instability of a continuously stratified atmosphere

Abstract The quasi‐geostrophic equation is solved numerically in the troposphere to identify growing modes associated with baroclinic instability. The classical Eady result is recovered on the ‐plane. However, on the ‐plane, significant deviations from both the Eady solution and the two‐layer Phillips model are observed, affecting growth rates and modal structures. Numerical simulations reveal the emergence of unstable lobes and the presence of a stable region at very large wavelengths, the extent of which depends on the ‐effect. The critical shear predicted by the two‐layer model is not observed; instead, peak instability shifts toward shorter wavelengths as the system approaches the Equator. A comparison of linear and nonlinear simulations under different initial conditions shows consistent behavior, suggesting that nonlinear interactions do not alter the instability growth significantly. Furthermore, in more realistic scenarios that account for variations in density stratification and surface friction, the unstable regions exhibit a broader spatial distribution, while the growth rate is reduced.