A Finite-Amplitude Eliassen-Palm Theorem in Isentropic Coordinates

Abstract

Isentropic coordinates are used to generalize to finite amplitude the celebrated theorem (1.1) of Eliassen and Palm(1961),under non-acceleration conditions. This primitive-equation result also generalizes the finite-amplitude quasi-geostrophic result of Edmon et at. (1980). A simple physical interpretation is provided, and a set of transformed Eulerian-mean equations arises naturally in the course of the analysis. Isentropes which intersect the lower boundary need special attention; the technique developed to handle them is a generalization of an idea due to Lorenz (1955), and may be of use in other contexts. Mention is also made of a version of the theorem valid for small-amplitude, transient, non-conservative disturbances.