On the existence of Arnold-stable barotropic flows on a rotating sphere

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Application of two well-known finite-amplitude stability conditions by Arnold to two-dimensional flows on a rotating sphere is discussed, in the context of the barotropic vorticity equation. Attention is focused on zonal basic flows with nonmonotonic profiles of absolute vorticity, since for such flows stability would not descend from the Rayleigh-Kuo inflection point theorem. It is shown that global flows of this kind cannot satisfy either of Arnold's stability conditions. © 2003 American Institute of Physics.
Original languageEnglish
Pages (from-to)3879 - 3882
Number of pages4
JournalPhysics of Fluids
Issue number12
Publication statusPublished - Dec 2003
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

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