Exponential approximations for the primitive equations of the ocean

Temam, Roger M.; Wirosoetisno, Djoko

Abstract

We show that in the limit of small Rossby number \varepsilon, the primitive equations of the ocean (OPEs) can be approximated by "higher-order quasi-geostrophic equations'' up to an exponential accuracy in \varepsilon. This approximation assumes well-prepared initial data and is valid for a timescale of order one (independent of \varepsilon). Our construction uses Gevrey regularity of the OPEs and a classical method to bound errors in higher-order perturbation theory.

Citation

Temam, R. M., & Wirosoetisno, D. (2007). Exponential approximations for the primitive equations of the ocean. Discrete and Continuous Dynamical Systems - Series B, 7(2), 425-440. https://doi.org/10.3934/dcdsb.2007.7.425

• Journal Article Type: Article
• Publication Date: 2007-03
• Deposit Date: Feb 29, 2008
• Journal: Discrete and Continuous Dynamical Systems - Series B
• Print ISSN: 1531-3492
• Electronic ISSN: 1553-524X
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 2
• Pages: 425-440
• DOI: https://doi.org/10.3934/dcdsb.2007.7.425
• Keywords: Singular perturbation, Exponential asymptotics, Gevrey regularity, Primitive equations.
• Public URL: https://durham-repository.worktribe.com/output/1579273
• Publisher URL: http://www.aimsciences.org/journals/pdfs.jsp?paperID=2142&mode=abstract