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Resolution effects and enslaved finite-difference schemes for a double gyre, shallow-water model. (English) Zbl 0912.76042

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. We present a method applicable to any finite-difference scheme, which effectively increasees 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 scheme computed at twice the resolution.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography

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