Hayashi, Y., 1987: A modification of the atmospheric energy cycle. Journal of the Atmospheric Sciences, 44(15), 2006-2017.

Abstract: A modification is made of the conventional energy cycle by combining the eddy flux convergence and the mean meridional circulation terms in the mean momentum and heat equations. The combined terms are interpreted as the effective flux convergences in the extratropics where the steady state mean circulation is regarded as essentially being induced by eddies. In the presence of mean heating, the modified energy cycle is simpler and less misleading than the transformed energy cycle based on the transformed Eulerian-mean equations.
This modification suggests that the major energy source of tropospheric planetary waves can be traced to the thermal generation of mean potential energy and that the stratospheric planetary wave is maintained by the total (mean plus eddy) vertical flux of energy from the troposphere. The conventional energy cycle of observed tropospheric planetary waves is, however, not as complicated as that of theoretical planetary waves in the quasi-nonacceleration condition. This is due to the fact that the observed tropospheric eddy heat flux convergence is counterbalanced by the mean heating and does not induce a large mean circulation in the steady state.