The traditional derivation of the energy cycle is reviewed and some paradoxical properties of the energy conversion and flux terms under non-acceleration conditions (steady, conservative motion) are noted. An alternative scheme is derived, based on the transformed Eulerian-mean system of Andrews and McIntyre (1976). The structure of this scheme is somewhat different from that of the traditional form (e.g., the only mean-to-eddy conversion term is through the kinetic energies) and the individual definitions of energy conversion and flux terms, and of eddy potential energy, differ from their counterparts in the traditional scheme. Thew differences are manifested most dramatically under non-acceleration conditions, but the qualitative differences are substantial even when these conditions are not met.
Comparison between the two schemes provides insight into the limitations of energy diagnostics. It is argued that the physical interpretations sometimes associated with individual components of the energy cycle and with the overall structure of the cycle are not generally valid.