Energetics in the Charney Problem with a Generic Stratosphere

This paper reports a complete diagnosis of energetics of the three representative structurally distinct unstable modes in the Charney problem with a generic stratosphere presented in Mak et al (2021). The diagnosis of the vertically-local-energetics of these modes (Charney+ mode, Green mode and Tropopause mode) helps delineate the physical nature of the impacts of a tropopause upon their vertical structures. The total-energetics diagnosis reveals that the computational noise is negligible in the significantly unstable modes, but that in a weakly unstable mode is measurable. Treating the top boundary as a sufficiently high free-surface adequately permits the existence of vertically propagating modes with negligibly small energy passing through it. The analysis of this generalized Charney problem could be relevant to the study of troposphere-stratosphere interaction capable of inducing anomalous tropospheric weather regimes.