Based on the coherent superposition principle and the generalized Huygens-Fresnel diffraction integral, the properties of a radial beam array with definite initial phase distributions propagating through a turbulent atmosphere are analytically investigated. It is shown that, when the propagation distance is short, the output intensity distribution will gradually take on a spiral shape, which means an optical vortex. However, under the effect of the atmospheric turbulence, the output vortex property gradually disappears, and changes to a bright-cantered beam without vortex property. Furthermore, the weaker the atmospheric turbulence is, the longer distance the output optical vortex （the center-dark beam） can propagate over.