Summary
The necessary and sufficient condition for the real value of the baroclinic frequency is that the axis of the developing wave should have no tilt along the vertical (when the amplitude of perturbation is zero at the boundaries). Also, if the boundary value of the amplitude of the perturbation is non-zero, the tilted axis of the wave does not always indicate baroclinic instability.
The above conclusions are equally applicable to the barotropic instability of zonal flow in equivalent barotropic model. Also, the necessary condition of barotropic instability of zonal flow in the equivalent barotropic model is obtained when the axis of the wave is tilted and boundary-amplitude of the eddy is zero.
Zusammenfassung
Die notwendige und hinreichende Bedingung für den realen Wert der baroklinen Frequenz ist, daß die Achse der sich entwickelnden Welle keine Neigung in der Vertikalen haben sollte (wenn die Amplitude der Störungen an den Grenzen Null ist). Auch wenn der Grenzwert der Amplitude der Störung nicht Null ist, zeigt die geneigte Achse der Welle nicht immer eine, barokline Instabilität an.
Die obigen Folgerungen sind in gleicher Weise auf die barotrope Instabilität der zonalen Strömung im äquivalent barotropen Modell anwendbar. Die notwendige Bedingung der barotropen Instabilität der zonalen Strömung im äquivalent barotropen Modell besteht auch, wenn die Achse der Welle geneigt ist und die Grenzamplitude des Wirbels Null ist.
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Mahanti, A.C. Some discussions on the baroclinic and barotropic instabilities over Indian region during summer. Arch. Met. Geoph. Biocl. A. 32, 87–96 (1983). https://doi.org/10.1007/BF02272713
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DOI: https://doi.org/10.1007/BF02272713