### Abstract

We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the "slow" ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the "slow" ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations.

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

Pages (from-to) | 143-159 |

Number of pages | 17 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 13 |

Issue number | 2 |

State | Published - 1999 |

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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*,

*13*(2), 143-159.

**A numerical study of an operator splitting method for rotating flows with large ageostrophic initial data.** / Jones, Donald; Mahalov, Alex; Nicolaenko, Basil.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 13, no. 2, pp. 143-159.

}

TY - JOUR

T1 - A numerical study of an operator splitting method for rotating flows with large ageostrophic initial data

AU - Jones, Donald

AU - Mahalov, Alex

AU - Nicolaenko, Basil

PY - 1999

Y1 - 1999

N2 - We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the "slow" ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the "slow" ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations.

AB - We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the "slow" ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the "slow" ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations.

UR - http://www.scopus.com/inward/record.url?scp=0033238477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033238477&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033238477

VL - 13

SP - 143

EP - 159

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 2

ER -