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

Donald Jones, Alex Mahalov, Basil Nicolaenko

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish (US)
Pages (from-to)143-159
Number of pages17
JournalTheoretical and Computational Fluid Dynamics
Issue number2
StatePublished - 1999

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes


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