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| Titel |
The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets |
| VerfasserIn |
A. M. Balk |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 21, no. 1 ; Nr. 21, no. 1 (2014-01-10), S.49-59 |
| Datensatznummer |
250120874
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| Publikation (Nr.) |
 copernicus.org/npg-21-49-2014.pdf |
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| Zusammenfassung |
We consider an adiabatic-type (approximate) invariant that was earlier
obtained for the quasi-geostrophic equation and the shallow water system; it
is an extra invariant, in addition to the standard ones (energy, enstrophy,
momentum), and it is based on the Rossby waves. The presence of this
invariant implies the energy transfer from small-scale eddies to large-scale
zonal jets.
We show that this extra invariant can be extended to the dynamics of a
three-dimensional (3-D) fluid layer on the beta plane. Combined with the
investigation of other researchers, this 3-D extension implies enhanced
generation of zonal jets.
For a general physical system, the presence of an extra invariant (in
addition to the energy–momentum and wave action) is extremely rare. We
summarize the unique conservation properties of geophysical fluid dynamics
(with the beta effect) that allow for the existence of the extra invariant,
and argue that its presence in various geophysical systems is a strong
indication that the formation of zonal jets is indeed related to the extra
invariant.
Also, we develop a new, more direct, way to establish extra invariants
(without using cubic corrections). For this, we introduce the small
denominator lemma. |
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