Slow Manifolds and Invariant Sets of the Primitive Equations

R. Temam, D. Wirosoetisno
2011 Journal of the Atmospheric Sciences  
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more » ... full DRO policy for further details. 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.
doi:10.1175/2010jas3650.1 fatcat:nipek3j5sfbshgl5ncuwvjx4ja