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The Barotropic Mode for the Primitive Equations

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Abstract

The barotropic mode of the Primitive Equations is considered. The corresponding equations resemble the Euler equations of incompressible flows with marked differences. The existence and uniqueness of solutions for the linearized equations is proven; the proof is based on the study of a nonstandard boundary value problem. In the nonlinear case, several schemes inspired by the projection method are proposed and their stability is studied. Finally, numerical simulations are described using one of these schemes, closely related to the pressure correction projection scheme.

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Authors and Affiliations

  1. Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA

    Qingshan Chen, Ming-Cheng Shiue & Roger Temam

  2. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA

    Qingshan Chen

Authors
  1. Qingshan Chen
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  2. Ming-Cheng Shiue
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  3. Roger Temam
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Correspondence to Qingshan Chen.

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Chen, Q., Shiue, MC. & Temam, R. The Barotropic Mode for the Primitive Equations. J Sci Comput 45, 167–199 (2010). https://doi.org/10.1007/s10915-009-9343-8

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  • DOI: https://doi.org/10.1007/s10915-009-9343-8

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