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The stability of small amplitude Rossby waves in a channel

Published online by Cambridge University Press:  11 April 2006

R. A. Plumb
R. A. Plumb
Affiliation:
Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire Present address: CSIRO, Division of Atmospheric Physics, Aspendale, Victoria 3195, Australia.
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Abstract

The breakdown of Rossby waves in a bounded system is studied for the case in which the wave amplitude is small. In a very long, laterally bounded, channel all waves are unstable via second-order resonant interactions except those of wavenumber π/L in the cross-channel direction (where L is the channel width), which are stable if their longitudinal wavenumber is greater than 0·681π/L. These waves are, however, unstable to weaker side-band interactions, so that all waves with non-zero longitudinal wavenumber are unstable. The transition from sideband to triad instability occurs where the group velocity of the basic wave is equal to the velocity of long waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 4 , 23 May 1977 , pp. 705 - 720
Copyright
© 1977 Cambridge University Press

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