Fast wave averaging for the equatorial Shallow Water equations

Alexandre Dutrifoy, Andrew Majda

Research output: Contribution to journalArticlepeer-review


The equatorial shallow water equations in a suitable limit are shown to reduce to zonal jets as the Froude number tends to zero. This is a theorem of a singular limit with a fast variable coefficient due to the vanishing of the Coriolis force at the equator. Although it is not possible to get uniform estimates in classical Sobolev spaces (other than L2) by differentiating the system, a new method exploiting the particular structure of the fast coefficient leads to uniform estimates in slightly different functional spaces. The computation of resonances shows that fast waves may interact with a strong external forcing, introduced to mimic the effects of moisture, to create zonal jets.

Original languageEnglish (US)
Pages (from-to)1617-1642
Number of pages26
JournalCommunications in Partial Differential Equations
Issue number10
StatePublished - Oct 2007


  • Equatorial shallow water equations
  • Fast averaging
  • Singular limit
  • Zonal jets

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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