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We present an analysis of the short-term modulation (one rotation of Bartels-27 days) of the galactic cosmic rays (GCR) by the solar wind, based on the cosmic ray rates observed by the Pierre Auger Observatory (PAO) on their surface detectors in scaler mode. The incidence of GCR with energies below $\sim$ 50 TeV, at the top of the atmosphere, produces more than 90\% of the secondary particles registered at ground level, i.e., they are subject to solar modulation. The modulation is consistent with at least two components: The first is the modulation of the amplitude of the cosmic rays diurnal variation, anti-correlated with the solar-wind speed. The second one occurs during the high-speed stream (HSS), the baseline of the cosmic rays diurnal variation train falls, following the time profile of the solar-wind speed inversely. Based on the radial gradient of the cosmic ray diffusion theory and under some other premises, such as the latitude dependence on diurnal variation and the inclusion of drift processes in the propagation of GCR, a semi-empirical description of the modulation is possible to do, and it hereafter is called as Toy-model. Although the Toy-model does not include fluctuations due to propagation in the atmosphere, it provides satisfactory results when compared with the PAO scaler mode data. We present details of these observations as well as the Toy-model validation.