Vacillation, sudden warmings and potential enstrophy balance in the stratosphere

The balance of potential enstrophy and its relationship to vacillation cycles and the sudden warming is studied for a beta-channel model of the stratosphere. It is shown that the mean flow cannot be steady in the presence of large-amplitude quasi-geostrophic waves (approximately 1-0.25 geopotential kilometers /gpkm/) when any dissipation is present, and the maximum wave amplitude allowed is approximately 2 gpkm. If wave forcing (transience plus dissipation) is artificially maintained, the mean flow decelerates slowly at first then explosively as the potential vorticity gradient of the basic state is wiped out over the channel. This process is called wave saturation. The initial phase of the explosive deceleration resembles both the observed and modeled mean flow evolution during a sudden stratospheric warming. A simple vacillation model based upon these ideas shows remarkable similarity to the results of Holton and Mass (1976) and Davies (1981).