Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans
The properties of the instability of combined gravity-inertial-Rossby waves on a β-plane are investigated. The wave-energy exchange equation shows that there is an exchange of energy with the background stratified medium. The energy source driving the instability lies in the background enthalpy...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2011-06-01
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| Series: | Annales Geophysicae |
| Online Access: | https://www.ann-geophys.net/29/997/2011/angeo-29-997-2011.pdf |
| Summary: | The properties of the instability of combined gravity-inertial-Rossby waves
on a β-plane are investigated. The wave-energy exchange equation shows
that there is an exchange of energy with the background stratified medium.
The energy source driving the instability lies in the background enthalpy
released by the gravitational buoyancy force.
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It is shown that if the phase speed of the westward propagating low
frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or
"equivalent" shallow water) wave speed, instability arises from the merging
of Rossby and Poincaré modes. There are two key parameters in this
instability condition; namely, the equatorial/rotational Mach (or Froude)
number <I>M</I> and the latitude θ<sub>0</sub> of the β-plane. In general waves
equatorward of a critical latitude for given <I>M</I> can be driven unstable, with
corresponding growth rates of the order of a day or so. Although these
conclusions may only be safely drawn for short wavelengths corresponding to a
JWKB wave packet propagating internally and located far from boundaries,
nevertheless such a local instability may play a significant role in
atmosphere-ocean dynamics. |
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| ISSN: | 0992-7689 1432-0576 |