Topographically Induced Stationary Solutions of Linearized Shallow Water Equations on Various Grids

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  • 1 Federal Hydrometeorological Institute, Belgrade, Yugoslavia
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Abstract

The effect of the grid choice on the stationary solutions of the linearized shallow water equations in the presence of topography is examined.

The time-averaged numerical solutions on the C grid reported by Arakawa and Lamb as well as the B-grid solutions of Dragosavac et al. may be considered to belong to this class. Namely, due to the time-averaging, the transient motions are, to a large extent, filtered out, leaving behind the predominantly stationary part. The absolute values of the ratios of the amplitudes of the finite-difference and exact solutions have been chosen as the measure of the error introduced by the finite-differencing.

The results obtained suggest that with reasonable resolution the horizontal space arrangement of dependent variables may affect the finite-difference solutions on the synoptic scales.

Abstract

The effect of the grid choice on the stationary solutions of the linearized shallow water equations in the presence of topography is examined.

The time-averaged numerical solutions on the C grid reported by Arakawa and Lamb as well as the B-grid solutions of Dragosavac et al. may be considered to belong to this class. Namely, due to the time-averaging, the transient motions are, to a large extent, filtered out, leaving behind the predominantly stationary part. The absolute values of the ratios of the amplitudes of the finite-difference and exact solutions have been chosen as the measure of the error introduced by the finite-differencing.

The results obtained suggest that with reasonable resolution the horizontal space arrangement of dependent variables may affect the finite-difference solutions on the synoptic scales.

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