Conservation laws of wave action and potential enstrophy for rossby waves in a stratified atmosphere

The purpose of this article is to discuss the evolution of wave energy, enstrophy and action for atmospheric Rossby waves in a variable mean flow. The presentation is theoretical, but does not represent original research; rather, it is pedagogic in nature. The work of a number of people has been drawn together into a unified account, with much of the algebra implicit in previous work made explicit here. The central results are that wave energy is conserved only when there are no spatial variations in the mean flow, and wave action is conserved even in the presence of such variations as long as they are not in the longitudinal direction. Finally, wave enstrophy is conserved in the presence of arbitrary (slow) mean flow variations.