| The normal modes of large-scale atmospheric motions have been examined in a spherical quasi-geostrophic model extending from the surface up to 80 km to investigate the stability of zonal motions in the stratosphere and mesosphere. Two sets of calculations were performed.;In the second set, a comparison is made of the stabilities of the stratospheric basic states before and after the 1976/1977 sudden warming event. Before the sudden warming, waves 1 and 2 were almost stationary. They are identified as the deep Green modes with their maximum geopotential amplitude in the upper stratosphere. Wave 3 could also reach the upper stratosphere but had maximum amplitude in the troposphere. After the sudden warming, the planetary waves 1, 2 and 3 were all confined to the troposphere, resembling the external Charney mode, and propagated with a much larger phase speed. The associated energetics in the stratosphere underwent a reversal from a typical baroclinic energy conversion (before the sudden warming) to the opposite conversion (after the sudden warming). These characteristics of transient planetary waves and the associated energetics agree fairly well with the observations.;In the first set, the basic states are representative of the Northern Hemisphere winter and summer solstice conditions. The winter basic state is able to support baroclinically unstable, quasi-stationary planetary waves 1 and 2, which extend into the stratosphere and the mesosphere from the troposphere at high latitudes. They are identified as Green modes. The structure of the unstable Green mode compares favorably with the observed quasi-stationary planetary waves. Waves 4-6, generated in the troposphere, can also penetrate into the lower stratosphere but are trapped there and resemble Charney modes. Energetics analysis indicates that the ratio of the local energy conversion versus energy flux from below is about 1:2 for the Green modes waves 1 and 2 in the stratosphere while the mean flow and the planetary waves in the mesosphere are all supported by wave energy flux from below. In summer, the unstable normal mode solutions are significant only either in the troposphere or in the mesosphere, with little amplitude in the stratosphere. The mesosphere supports westward propagating waves 1-4, especially wavenumber 3, which may be identified as a 2-day wave observed in the summer mesosphere. |
