Large-Amplitude nonlinear stability results for atmospheric circulations

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Type Article
Original languageEnglish
Pages (from-to)1969-1988
Number of pages20
JournalQuarterly Journal of the Royal Meteorological Society
Volume129
Issue number591
DOI
Publication statusPublished - Apr 2003
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Abstract

It is shown how large-amplitude stability results for flows governed by potential-vorticity conservation can be obtained by geometric arguments using rearrangements of functions. The method allows for non-smooth solutions, and also gives a framework for the rigorous treatment of the effects of mixing by increasingly fine-scale filamentation. It is, thus, different from the energy-Casimir method. It is applied to the semi-geostrophic shear-flow problem in a channel, where the results can be compared with other methods. It is shown that, under the definitions used, there are no non-zonal nonlinearly-stable states in this problem. In the baroclinic case, it is shown how potential-vorticity conservation reduces the available energy for the transient flow. Copyright © 2003 Royal Meteorological Society

Keywords

  • Hamiltonian, Potential vorticity, Rearrangements