Baroclinic instability on a sphere in two‐layer models

The baroclinic instability problem is studied for various two‐layer zonal velocity profiles on a sphere for both quasi‐geostrophic (P) and modified‐geostrophic (L) models, the latter containing nongeostrophic advection of temperature. Critical amplitudes for instability and other properties for the rigid rotation profile are obtained for a wide range of values of the static stability, and results of previous studies on the sphere are related and shown to be mutually consistent. Critical amplitudes are also obtained for some jet profiles, and unstable midlatitude jet profiles with values of the static stability and shear representative of the atmosphere are studied in detail. In particular it is found for the latter that heat fluxes (in the L model) are larger in the lower layer than in the upper, and that their equatorward components (at high and low latitudes) are small; also, there are no growing modes with large equatorial flows as found for the rigid rotation profile. A simple hypothesis which relates the pattern of momentum fluxes to the β‐plane stability criterion, and is consistent with all known results, is proposed. The results, particularly growth rates and stream functions, are compared with those of simplified and multilevel models. For the most unstable mode the differences between the two‐layer and multilevel results are not as large as might be expected on the basis of previous studies, and reasons for this are stated.