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| Titel |
Propagation properties of Rossby waves for latitudinal β-plane variations of f and zonal variations of the shallow water speed |
| VerfasserIn |
C. T. Duba, 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 ; 30, no. 5 ; Nr. 30, no. 5 (2012-05-15), S.849-855 |
| Datensatznummer |
250017226
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| Publikation (Nr.) |
 copernicus.org/angeo-30-849-2012.pdf |
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| Zusammenfassung |
| Using the shallow water equations for a rotating layer of fluid, the wave and dispersion equations for Rossby waves
are developed for the cases of both the standard β-plane approximation for the latitudinal variation of the
Coriolis parameter f and a zonal variation of the shallow water speed. It is well known that the wave normal diagram for the
standard (mid-latitude) Rossby wave on a β-plane is a circle in wave number (ky,kx) space, whose
centre is displaced −β/2 ω units along the negative kx axis, and whose radius is less than this displacement, which means that phase
propagation is entirely westward. This form of anisotropy (arising from the
latitudinal y variation of f), combined with the highly dispersive nature of the wave, gives rise to a group
velocity diagram which permits eastward as well as westward propagation. It is shown that the group velocity
diagram is an ellipse, whose centre is displaced westward, and whose major and minor axes give the
maximum westward, eastward and northward (southward) group speeds as functions of the frequency and a parameter
m which measures the ratio of the low frequency-long wavelength Rossby wave speed to the shallow water speed. We
believe these properties of group velocity diagram have not been elucidated in this way before. We present a
similar derivation of the wave normal diagram and its associated group velocity curve for the case of a zonal
(x) variation of the shallow water speed, which may arise when the depth of an ocean varies zonally from a
continental shelf. |
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