Free gravity waves and balanced dynamics

Wirosoetisno, D., Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 and Temam, R. M. (2002) Free gravity waves and balanced dynamics. Journal of the Atmospheric Sciences, 59. pp. 3382-3398. ISSN 1520-0469 doi: 10.1175/1520-0469(2002)059<3382:FGWABD>2.0.CO;2

Abstract/Summary

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/32215
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Meteorological Society
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