### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 269-280 |

Number of pages | 12 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 9 |

Issue number | 3-4 |

State | Published - 1997 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Theoretical and Computational Fluid Dynamics*,

*9*(3-4), 269-280.

**Resolution effects and enslaved finite-difference schemes for a double gyre, shallow-water model.** / Jones, Donald; Poje, Andrew C.; Margolin, Len G.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 9, no. 3-4, pp. 269-280.

}

TY - JOUR

T1 - Resolution effects and enslaved finite-difference schemes for a double gyre, shallow-water model

AU - Jones, Donald

AU - Poje, Andrew C.

AU - Margolin, Len G.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041194600&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041194600&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041194600

VL - 9

SP - 269

EP - 280

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 3-4

ER -