Rossby Normal Modes in Nonuniform Background Configurations. Part II. Equinox and Solstice Conditions

Abstract

The existence of planetary normal modes in the presence of realistic mean fields is examined. For sufficiently large wavenumber m, or meridional index n, the response of the Rossby modes is diffused beyond identification. This is primarily a result of the Doppler shifting of mean winds and supersedes the increasing role of dissipation. Several initial modes for the first few wavenumbers should be both realizable and identifiable in typical conditions. ?At least? the first three modes of wavenumber 1, the first two of wavenumber 2, and the first of wavenumber 3 should occur with periods isolated to within 12.5% of median values. The mode structures for the first four modes of wavenumbers 1, 2 and 3 are insensitive to the mean fields in the lowest two scale heights. In addition, the response of each of these is readily discernable in both equinox and solstice conditions. The modes' horizontal character is notably robust. Although the solutions typically exhibit regions where they are affected by the mean fields, the domain of influence is local. Vertical growth rates tend to be magnified in regions where the winds are weak westerly relative to the wave or the temperature gradient is equatorward, while amplitudes evanesce in regions of strong westerlies or poleward temperature gradient. The former give rise to enhanced amplitudes in the equinox stratosphere and the summer mesosphere. Results calculated here for the first symmetric wavenumber 1 mode are in close agreement with those found by Geisler and Dickinson (1976). Moreover, the estimate for the possible spread of variance compares favorably with the 4?6 day range existing in the observational evidence. Calculations for the second symmetric wavenumber 1 mode support Madden's (1978) identification of the 16-day wavenumber 1 disturbance with the (m, n ? m)=(1, 3) mode. In the presence of uniform surface forcing, the peak response is very near 16 days. More importantly, the estimate of possible spread in variance is compatible with the observed 1?3 week range for the disturbance. Although its structure is largely unaffected in the first few scale heights, the mode attains large amplitudes in the winter stratosphere of the solstice configuration. Finally, a number of observed features of the 2-day wave in the upper atmosphere suggest its identification with the third Rossby-gravity mode, which corresponds well in both temporal and spatial character.