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Symmetric Stability of Compressible Zonal Flows on a Generalized Equatorial [beta] Plane
- Article from:
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Journal of the Atmospheric Sciences
- Article date:
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June 1, 2008
- Author:
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Copyright informationCopyright American Meteorological Society Jun 2008. Provided by ProQuest LLC. (Hide copyright information)
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ABSTRACT
Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial β plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector.
A version of the energy-Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity ...