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We report the results of the numerical simulation of an atmospheric-pressure nitrogen plasma jet with the focus on the downstream kinetics. The goal is to assess the effect of ambient air on the spatial profile of reactive species densities of the plasma jet. The modeling results show that oxygen readily enters the jet downstream, and the excited-state nitrogen densities decrease drastically with the interaction of oxygen and the jet. A direct comparison of the spatial profile of the excited-state nitrogen density (N2B3Πg) and the visual appearance of the plasma jet obtained experimentally shows that the model qualitatively captures the change of the jet size when the jet is in contact with ambient air.