Rossby Normal Modes in Nonuniform Background Configurations. Part I: Simple Fields

Abstract

The influence of mean field variations on the realization of planetary normal modes is investigated by examining the mode response and structure in the presence of simple background nonuniformities. Gradients in the mean wind and temperature fields have the collective effect of depressing, shifting and broadening the characteristic response. While nonuniformities in both the wind and temperature fields contribute to the reduction in resonant response, spectral shifting and broadening are induced principally by variations in the mean wind field. The eigenperiods, for the most part, are influenced by the mean winds in the lowest three scale heights. The characteristic structure is modified through a change in evanescence according to the local index of refraction. In regions of reduced refractive index, for example, strong westerlies relative to the wave or a poleward temperature gradient, the mode's vertical growth rate is retarded. Conversely, in regions of increased refractive index, for example, weak westerlies relative to the wave or an equatorward temperature gradient, the vertical growth of amplitude is enhanced. Amplitudes decay sharply into regions where the winds are easterly relative to the wave (negative refractive index). While the vertical character is sensitive to the mean fields throughout, the horizontal structure is influenced only locally. This robust nature of the eigenstructure prevails in even the most drastic simple configurations, e.g., when absorbing critical surfaces are present. A general decline in the characteristic response results with increasing mean field variation. The same tendency is observed as the region of nonuniformity is moved to lower levels and lower latitudes. No appreciable change in the global response occurs with the introduction of a critical surface aloft. The various influences which degrade the resonant response increase with wavenumber m and meridional index n. Hence in realistic conditions, the response of the Rossby modes will necessarily be suppressed and diffused beyond identification for sufficiently large m or n.