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Baroclinic Instability of the Zonal Wind: Part II

John W. MilesInstitute of Advanced Studies, Australian National University, Canberra, Australia

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Abstract

An approximate solution of the eigenvalue problem governing the stability of the zonal wind with respect to small disturbances of long wavelength is developed for profiles with strong, positive-definite vertical shear. It is found that certain disturbances, characterized by positive phase velocities, appear to be stable on the basis of a first approximation but are unstable in higher approximations. The results, together with the previously established instability for short wavelengths and/or weak vertical shear, support the conjecture that typical zonal-wind configurations are unstable with respect to small disturbances of almost all wavelengths at almost all windspeeds.

Abstract

An approximate solution of the eigenvalue problem governing the stability of the zonal wind with respect to small disturbances of long wavelength is developed for profiles with strong, positive-definite vertical shear. It is found that certain disturbances, characterized by positive phase velocities, appear to be stable on the basis of a first approximation but are unstable in higher approximations. The results, together with the previously established instability for short wavelengths and/or weak vertical shear, support the conjecture that typical zonal-wind configurations are unstable with respect to small disturbances of almost all wavelengths at almost all windspeeds.

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