ON THE NON-EXISTENCE OF CRITICAL WAVELENGTHS IN A CONTINUOUS BAROCLINIC STABILITY PROBLEM
- 1 January 1962
- journal article
- Published by American Meteorological Society in Journal of the Atmospheric Sciences
- Vol. 19 (1) , 31-38
- https://doi.org/10.1175/1520-0469(1962)019<0031:otneoc>2.0.co;2
Abstract
The baroclinic stability problem relating to a Couette west-wind profile over a flat topography and extending to infinite height on the rotating earth is treated in the β-plane formulation, as presented by Charney and Kuo. It is shown by analytical methods that the concept of a critical wavelength, separating unstable from neutral waves, is not applicable in this case, and that, with the exception of a finite number of isolated wavelengths, all wavelengths have an exponentially unstable mode associated with them, together with no or a finite number of neutral regular modes. A limiting procedure for vanishing friction, using Wasow's singular perturbation theory, establishes that all unstable solutions are relevant to the problem.Keywords
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