A new physical hypothesis predicts that a weak coupling of the orbital and rotational motions of extended bodies may give rise to a modulation of circulatory flows within their atmospheres. Driven cycles of intensification and relaxation of large-scale circulatory flows are predicted, with the phasing of these changes linked directly to the rate of change of the orbital angular momentum with respect to inertial frames. We test the hypothesis that global-scale dust storms (GDS) on Mars may occur when periods of circulatory intensification (associated with positive and negative extrema of the waveform) coincide with the southern summer dust storm season on Mars. The orbit-spin coupling hypothesis additionally predicts that the intervening transitional periods, which are characterized by the disappearance and subsequent sign change of this waveform, may be unfavorable for the occurrence of GDS, when they occur during the southern summer dust storm season. These hypotheses are confirmed through comparisons between calculated dynamical time series of the time rate of change of orbital angular momentum and historic observations. All of the nine known global-scale dust storms on Mars took place during Mars years when circulatory intensification during the dust storm season is predicted under the orbit-spin coupling hypothesis. No historic global-scale dust storms were recorded during transitional intervals. Orbit-spin coupling accelerations evidently contribute to the interannual variability of the Mars atmosphere.