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Generalized Eady waves

Published online by Cambridge University Press:  29 March 2006

Gareth P. Williams
Gareth P. Williams
Affiliation:
Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, New Jersey
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Abstract

Solutions are obtained for the baroclinic instability problem for situations in which the static stability and mean shear vary geminately with height. The simple solution given by Eady is shown to be a special limiting case of a class of exact solutions for flows whose basic states have a vanishing interior potential vorticity gradient. The generalized solutions show that the temperature amplitude distribution is particularly sensitive to vertical variations in static stability but that phases and other amplitudes are only slightly influenced by such variations. When the static stability and shear increase (decrease) with height an enhanced temperature maximum occurs at the upper (lower) surface in comparison with the standard Eady solution.

The generalized solutions also help to explain the character of annulus waves and predict a short-wave cut-off that is the same as that given by Eady's theory provided that it is based on the vertically averaged gravitational frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 4 , 27 February 1974 , pp. 643 - 655
Copyright
© 1974 Cambridge University Press

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References

Eady, E. T. 1949 Long waves and cyclone waves Tellus, 1, 33–52.Google Scholar
Mcintyre, M. E. 1970 On the non-separable baroclinic parallel flow instability problem. J. Fluid Mech. 40, 273–306.Google Scholar
Stone, P. H. 1969 The meridional structure of baroclinic waves. J. Atmos. Sci. 26, 376–389.Google Scholar
Williams, G. P. 1971 Baroclinic annulus waves J. Fluid Mech. 49, 417–449.Google Scholar