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Large‐amplitude nonlinear stability results for atmospheric circulations
Author(s) -
Cullen M. J. P.,
Douglas R. J.
Publication year - 2003
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.01.196
Subject(s) - baroclinity , potential vorticity , filamentation , vorticity , nonlinear system , amplitude , stability (learning theory) , flow (mathematics) , transient (computer programming) , mechanics , geostrophic wind , mixing (physics) , classical mechanics , conservation law , meteorology , physics , mathematical analysis , mathematics , vortex , computer science , laser , quantum mechanics , machine learning , optics , operating system
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