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The non-linear instability of the two-dimensional slab symmetric disturbances of the dis-sipative system on the rotating earth subject to the forcing of the mean temperature field isinvestigated by means of the 5 modes low order truncated spectrum. We get the catastropheof the butterfly type. For a given definite value to the horizontal temperature gradient, withthe decrease of the static stability, the equilibrium state of the system generally proceeds start-ing from a quiescent single stable state, then abruptly jumping to the single stable state witha circulation of a certain strength, hereafter again residing stably in the double stable state ofstrong circulation. Moreover, there does not appear the periodic and non-periodic variation.Without temperature gradient, only a definite and comparatively weak vertical eddy viscosityin conjunction with the non-linear mechanism of the system itself and the linear static insta-bility of the environment can lead to the periodic or non-periodic variation.
The non-linear instability of the two-dimensional slab symmetric disturbances of the dis-sipative system on the rotating earth subject to the forcing of the mean temperature field is investigated by means of the 5 modes low order truncated spectrum. We get the catastrophe of the butterfly type. For a given definite value to the horizontal temperature gradient, with the decrease of the static stability, the equilibrium state of the system generally proceeds start-ing from a quiescent single stable state, then abruptly jumping to the single stable state witha circulation of a certain strength, hereafter again residing stably in the double stable state ofstrong circulation. Moreover, there does not appear the periodic and non-periodic variation. Without temperature gradient, only a definite and comparatively weak vertical eddy viscosityin conjunction with the non-linear mechanism of the system itself and the linear static insta-bility of the environment can lead to the periodic or non-periodi c variation