The Charney Baroclinic Stability Problem: Approximate Solutions and Modal Structures

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Abstract
The classic Charney baroclinic stability problem is examined through perturbation techniques in the short-wave limit, near the first neutral curve separating Charney and Green modes, and near the second neutral curve separating long and short Green modes. This method provides simple analytical expressions for the vertical structure of the growing waves and the dependence of phase speeds and growth rates on mean flow parameters. The rapidly growing Charney modes have horizontal and vertical scales which crucially depend on the β-parameter. Structures of heat and potential vorticity fluxes are also represented by approximate solutions and their dependence on wavenumber is examined.

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