Counter-propagating Rossby waves in the barotropic Rayleigh model of shear instability

E. Heifetz*, C. H. Bishop, P. Alpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


Wave development, using Rayleigh's 1880 model of barotropic, inviscid and incompressible flow, with a mean zonal wind which is linearly sheared between two edges, is described in terms of the interaction between two counter-propagating Rossby waves (CRWs). Although the solutions described by this approach could also be described by a sum of the normal modes originally obtained by Rayleigh, we offer a CRW description of Rayleigh's model because it provides a useful pedagogical framework for illustrating, in a precise and quantifiable manner, the interacting Rossby wave view of instability. A CRW interpretation of a modified version of the Rayleigh model, consisting of a jet-like flow featuring two strips of vorticity with opposite signs, is also given.

Original languageEnglish
Pages (from-to)2835-2853
Number of pages19
JournalQuarterly Journal of the Royal Meteorological Society
Issue number560
StatePublished - Oct 1999


  • Counter-propagating Rossby waves
  • Normal modes
  • Shear instability
  • Vorticity strips


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