## 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 language | English (US) |
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Pages (from-to) | 331-354 |

Number of pages | 24 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 19 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2005 |

## Keywords

- 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