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 journalArticle

Abstract

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
Volume19
Issue number5
DOIs
StatePublished - Oct 2005

Fingerprint

Climate models
Climate Models
climate models
barotropic wave
climate modeling
Rossby wave
conservation laws
planetary waves
baroclinic waves
energy
baroclinic mode
equatorial wave
baroclinic wave
Source Terms
Coriolis force
Conservation Laws
equators
hydrostatics
Conservation
wave packets

Keywords

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

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Oceanography
  • Computational Mechanics
  • Mechanics of Materials
  • Applied Mathematics
  • Physics and Astronomy(all)
  • Physics and Astronomy (miscellaneous)
  • Condensed Matter Physics

Cite this

A non-oscillatory balanced scheme for an idealized tropical climate model Part I : Algorithm and validation. / Khouider, Boualem; Majda, Andrew J.

In: Theoretical and Computational Fluid Dynamics, Vol. 19, No. 5, 10.2005, p. 331-354.

Research output: Contribution to journalArticle

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