The traditional approximation and equatorial inertial instability

The "traditional" hydrostatic approximation includes certain geometrical approximations necessary for retaining conservation of energy and absolute angular momentum principles, but the excluded terms are not so obviously negligible at the equator. For example, replacing the radial coordinate r with the Earth's radius a suppresses radial variations in the planetary angular momentum.

The importance of the neglected terms is investigated in the context of equatorial inertial instability, which is of relevance to the general circulation of the middle atmosphere. Various models on the equatorial beta plane are considered which are distinguished by the planetary contribution to the angular momentum. Both linear and nonlinear aspects of the instability are investigated.