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| Titel |
Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres |
| VerfasserIn |
J. F. McKenzie |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 27, no. 11 ; Nr. 27, no. 11 (2009-11-09), S.4221-4227 |
| Datensatznummer |
250016705
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| Publikation (Nr.) |
 copernicus.org/angeo-27-4221-2009.pdf |
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| Zusammenfassung |
| This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq
approximation. The wave equation for the system is fifth order in
space and time and demonstrates how gravity-inertial waves on
the one hand are coupled to Rossby waves on the other through the
combined effects of β, the stratification characterized by
the Väisälä-Brunt frequency N, the Coriolis
frequency f at a given latitude, and vertical propagation which
permits buoyancy modes to interact with westward propagating
Rossby waves. The corresponding dispersion equation shows that
the frequency of a westward propagating gravity-inertial wave is
reduced by the coupling, whereas the frequency of a Rossby wave is
increased. If the coupling is sufficiently strong these two modes
coalesce giving rise to an instability. The instability condition
translates into a curve of critical latitude Θc versus
effective equatorial rotational Mach number M, with the region
below this curve exhibiting instability. "Supersonic" fast
rotators are unstable in a narrow band of latitudes around the
equator. For example Θc~12° for Jupiter.
On the other hand slow "subsonic" rotators (e.g. Mercury, Venus
and the Sun's Corona) are unstable at all latitudes except very
close to the poles where the β effect vanishes.
"Transonic" rotators, such as the Earth and Mars, exhibit
instability within latitudes of 34° and
39°, respectively, around the Equator. Similar results
pertain to Oceans. In the case of an Earth's Ocean of depth 4km
say, purely westward propagating waves are unstable up to
26° about the Equator. The nonlinear evolution of this
instability which feeds off rotational energy and gravitational
buoyancy may play an important role in atmospheric dynamics. |
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