Based on the generalized Huygens-Fresnel principle and the modified von Karman spectrum model, the analytic expressions of the intensity distribution, the root mean square beam width and the power in the bucket of mutually-independent partially-coherent Gaussian-Shell model (GSM) array beams in the free space optics system are derived when the beams propagate in the atmospheric turbulence. The self-coupling characteristics, the power in the bucket and the beam spreading are analyzed numerically under the influence of different factors. The results show that when the partially coherent GSM array beams propagate for a certain distance in the atmospheric turbulence, they will be synthesized into a flat-topped beam which then evolves to a Gaussian beam. Moreover, the self-coupling characteristics of the array beams in atmospheric turbulence are better than those in free space. The influence of turbulent outer scale on the intensity distribution and beam spreading is very small, and can be ignored. Compared with the partially coherent single GSM beam, the partially coherent GSM array beams have stronger anti-turbulence properties, which is beneficial to realizing long-distance communications.