The Nonlinear Effects of Transient and Stationary Eddies on the Winter Mean Circulation. Part II: The Stability of Stationary Waves

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  • 1 Laboratory for Atmospheric Research, University of Illinois, Urbana 61801
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Abstract

A linear stability analysis was made for forced stationary planetary waves to supplement the theoretical interpretation on the large dissipative role of the transient motions, using simple quasi-geostrophic models on the midlatitude β-plane. For the simplest model in which the nonlinear effect is truncated by a triad interaction, the stability criteria are given by a pair of inequalities, the first of which specifies the critical amplitude of the basic state wave and the second the difference between the longitudinal and latitudinal wavenumber which are required for the perturbation to be unstable. The analysis for the two-layer baroclinic atmosphere suggests that the perturbations superimposed on the basic state with wavenumber three are likely to be unstable. The growth rate calculated from the model is compared favorably to the dissipation rate of the stationary wave due to the transient motions analysed in Part I.

Abstract

A linear stability analysis was made for forced stationary planetary waves to supplement the theoretical interpretation on the large dissipative role of the transient motions, using simple quasi-geostrophic models on the midlatitude β-plane. For the simplest model in which the nonlinear effect is truncated by a triad interaction, the stability criteria are given by a pair of inequalities, the first of which specifies the critical amplitude of the basic state wave and the second the difference between the longitudinal and latitudinal wavenumber which are required for the perturbation to be unstable. The analysis for the two-layer baroclinic atmosphere suggests that the perturbations superimposed on the basic state with wavenumber three are likely to be unstable. The growth rate calculated from the model is compared favorably to the dissipation rate of the stationary wave due to the transient motions analysed in Part I.

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