Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

H. R. Cho, T. G. Shepherd, V. A. Vladimirov

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The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjortoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows. By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities. The case of moist adiabatic systems is also considered. -from Authors

Original languageEnglish
Pages (from-to)822-836
Number of pages15
JournalJournal of the Atmospheric Sciences
Issue number6
Publication statusPublished - 1993


ASJC Scopus subject areas

  • Atmospheric Science

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