The Stability of a Nonlinear, Finite-Amplitude, Neutrally Stable Eady Wave

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  • 1 Department of Meteorology, Massachusetts Institute of Technology, Cambridge 02139
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Abstract

Lorenz's stability analysis of a finite-amplitude, barotropic Rossby wave is extended to a nonlinear, finite-amplitude, neutrally stable Eady wave with a vertical phase shift. For disturbances with a meridional wave-number less than the zonal wavenumber of the Eady wave, instability results from baroclinic and barotropic instability. For disturbances with a meridional wavenumber greater than the zonal wavenumber of the Eady wave, instability also occurs but results only from baroclinic instability. The most unstable mode occurs when the meridional wavelength of the perturbation is approximately twice the zonal wavelength of the Eady wave.

Abstract

Lorenz's stability analysis of a finite-amplitude, barotropic Rossby wave is extended to a nonlinear, finite-amplitude, neutrally stable Eady wave with a vertical phase shift. For disturbances with a meridional wave-number less than the zonal wavenumber of the Eady wave, instability results from baroclinic and barotropic instability. For disturbances with a meridional wavenumber greater than the zonal wavenumber of the Eady wave, instability also occurs but results only from baroclinic instability. The most unstable mode occurs when the meridional wavelength of the perturbation is approximately twice the zonal wavelength of the Eady wave.

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