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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31 Citations (Scopus)

Abstract

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
Volume50
Issue number6
Publication statusPublished - 1993

ASJC Scopus subject areas

  • Atmospheric Science

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