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Slow manifolds and invariant sets of the primitive equations.

Wirosoetisno, D. and Temam, R. (2011) 'Slow manifolds and invariant sets of the primitive equations.', Journal of the atmospheric sciences., 68 (3). pp. 675-682.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1175/2010JAS3650.1
Publisher statement:© 2011 American Meteorological Society
Date accepted:02 November 2010
Date deposited:17 February 2017
Date of first online publication:01 March 2011
Date first made open access:No date available

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