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In this study, an f-plane dynamical model for incompressible flows is presented to examine the mechanisms underlying the structure and stability of large-scale zonally symmetric circulations. Analyses based on the Principle of Exchange of Stabilities reveal that this zonally symmetric model possesses a single-cell structure in the absence of the Coriolis force, similar to the single-cell general atmospheric circulation in the absence of the Earth’s rotation as previously hypothesized. The circulation, however, bifurcates into a triple-cell structure in the presence of the Coriolis force if the vertical temperature gradient, the rotational rate, and the momentum eddy coefficients satisfy a certain constraint. Further analyses of this triple-cell structure as a result of the Coriolis force show that this structure is topologically stable, thus offering new insight into the highly resilient structure of the Earth’s atmospheric global circulations.