A non-oscillatory balanced scheme for an idealized tropical climate model Part I: Algorithm and validation

Boualem Khouider, Andrew J. Majda

Research output: Contribution to journalReview articlepeer-review


We propose a non-oscillatory balanced numerical scheme for a simplified tropical climate model with a crude vertical resolution, reduced to the barotropic and the first baroclinic modes. The two modes exchange energy through highly nonlinear interaction terms. We consider a periodic channel domain, oriented zonally and centered around the equator and adopt a fractional stepping-splitting strategy, for the governing system of equations, dividing it into three natural pieces which independently preserve energy. We obtain a scheme which preserves geostrophic steady states with minimal ad hoc dissipation by using state of the art numerical methods for each piece: The f-wave algorithm for conservation laws with varying flux functions and source terms of Bale et al. (2002) for the advected baroclinic waves and the Riemann solver-free non-oscillatory central scheme of Levy and Tadmor (1997) for the barotropic-dispersive waves. Unlike the traditional use of a time splitting procedure for conservation laws with source terms (here, the Coriolis forces), the class of balanced schemes to which the f-wave algorithm belongs are able to preserve exactly, to the machine precision, hydrostatic (geostrophic) numerical-steady states. The interaction terms are gathered into a single second order accurate predictor-corrector scheme to minimize energy leakage. Validation tests utilizing known exact solutions consisting of baroclinic Kelvin, Yanai, and equatorial Rossby waves and barotropic Rossby wave packets are given.

Original languageEnglish (US)
Pages (from-to)331-354
Number of pages24
JournalTheoretical and Computational Fluid Dynamics
Issue number5
StatePublished - Oct 2005


  • Barotropic-baroclinic nonlinear interactions
  • Large scale equatorial waves
  • Non-oscillatory balanced schemes
  • Precipitation fronts

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes


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