Euler equation on a fast rotating sphere - Time-averages and zonal flows

Bin Cheng, Alex Mahalov

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Motivated by recent studies in geophysical and planetary sciences, we investigate the PDE-analytical aspects of time-averages for barotropic, inviscid flows on a fast rotating sphere S 2. Of particular interest is the incompressible Euler equation. We prove that finite-time-averages of solutions stay close to a subspace of longitude-independent zonal flows. The initial data are unprepared and can be arbitrarily far away from this subspace. Our analytical study justifies the global Coriolis effect in the spherical geometry as the underlying mechanism of this phenomenon. We use Riemannian geometric tools including the Hodge theory in the proofs.

Original languageEnglish (US)
Pages (from-to)48-58
Number of pages11
JournalEuropean Journal of Mechanics, B/Fluids
StatePublished - Jan 2013


  • Barotropic models on a rapidly rotating sphere
  • Euler equations
  • PDE on surfaces
  • Rotating fluids
  • Time-averages
  • Zonal flows

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)


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