Resolution Effects and Enslaved Finite-Difference Schemes for a Double Gyre, Shallow-Water Model

We study numerical solutions of the reduced-gravity shallow-water equation on a beta plane, subjected to a sinusoidally varying wind forcing leading to the formation of a double gyre circulation. As expected the dynamics of the numerical solutions are highly dependent on the grid resolution and the...

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Bibliographic Details
Published in:Theoretical and computational fluid dynamics 1997-06, Vol.9 (3-4), p.269-280
Main Authors: Jones, Don A, Poje, Andrew C, Margolin, Len G
Format: Article
Language:English
Subjects:
Algorithms
Beta
Finite difference method
Fluid dynamics
Gyres
Marine
Mathematical analysis
Mathematical models
Shallow water
Statistics
Studies
Truncation errors
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Summary:We study numerical solutions of the reduced-gravity shallow-water equation on a beta plane, subjected to a sinusoidally varying wind forcing leading to the formation of a double gyre circulation. As expected the dynamics of the numerical solutions are highly dependent on the grid resolution and the given numerical algorithm. In particular, the statistics of the solutions are critically dependent on the scheme's ability to resolve the Rossby deformation radius. We present a method, applicable to any finite-difference scheme, which effectively increases the spatial resolution of the given algorithm without changing its temporal stability or memory requirements. This enslaving method makes use of properties of the governing equations in the absence of time derivatives to reduce the overall truncation error. By examining statistical measures of stochastic solutions at resolutions near the Rossby radius, we show that the enslaved schemes are capable of reproducing statistics of standard schemes computed at twice the resolution.
ISSN:0935-4964
1432-2250
DOI:10.1007/s001620050044