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Slow manifolds and invariant sets of the primitive equations

Wirosoetisno, D.; Temam, R.

Slow manifolds and invariant sets of the primitive equations Thumbnail


Authors

R. Temam



Abstract

The authors review, in a geophysical setting, several recent mathematical results on the forced–dissipative hydrostatic primitive equations with a linear equation of state in the limit of strong rotation and stratification, starting with existence and regularity (smoothness) results and describing their implications for the long-time behavior of the solution. These results are used to show how the solution of the primitive equations in a periodic box comes close to geostrophic balance as t → ∞. Then a review follows of how geostrophic balance could be extended to higher orders in the Rossby number, and it is shown that the solution of the primitive equations also satisfies a higher-order balance up to an exponentially small error. Finally, the connection between balance dynamics in the primitive equations and its global attractor, which is the only known invariant set (for a sufficiently general forcing), is discussed.

Citation

Wirosoetisno, D., & Temam, R. (2011). Slow manifolds and invariant sets of the primitive equations. Journal of the Atmospheric Sciences, 68(3), 675-682. https://doi.org/10.1175/2010jas3650.1

Journal Article Type Article
Acceptance Date Nov 2, 2010
Online Publication Date Mar 1, 2011
Publication Date Mar 1, 2011
Deposit Date Feb 17, 2011
Publicly Available Date Feb 17, 2017
Journal Journal of the Atmospheric Sciences
Print ISSN 0022-4928
Electronic ISSN 1520-0469
Publisher American Meteorological Society
Peer Reviewed Peer Reviewed
Volume 68
Issue 3
Pages 675-682
DOI https://doi.org/10.1175/2010jas3650.1

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Published Journal Article (515 Kb)
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Copyright Statement
© 2011 American Meteorological Society





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