Abstract
It has been shown previously how a transformation of coordinates applied to the primitive equations with the geostrophic momentum approximation produces the quite simple semi-geostrophic equations. Here the connection with quasi-geostrophic theory and the role of ageostrophic motions are clarified. The cross-frontal circulation equation of Eliassen (1962) is shown to be applicable in a modified form in three dimensions, and a simple “ω equation” in obtained.
A similar analytical development is possible in isentropic coordinates. As an example of the diagnostic use of the equations derived, a study of the formation of an upper air front in a numerical model is given.
