On the interpretation of Andrews’ theoremCarnevale, G. F. and Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1990) On the interpretation of Andrews’ theorem. Geophysical & Astrophysical Fluid Dynamics, 51 (1-4). pp. 1-17. ISSN 1029-0419 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1080/03091929008219847 Abstract/SummaryAndrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.
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