Abstract
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 with a circulation of a certain strength, hereafter again residing stably in the double stable state of strong circulation. Moreover, there does not appear the periodic and non-periodic variation. Without temperature gradient, only a definite and comparatively weak vertical eddy viscosity in 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.
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