  In this paper, we consider the effect of the atmospheric turbulence on the
propagation of optical vertex formed from the radial coherent laser beam array,
with the initially well-defined phase distribution. The propagation formula of
the radial coherent laser array passing through the turbulent atmosphere is
analytically derived by using the extended Huygens-Fresnel diffraction
integral. Based on the derived formula, the effect of the atmospheric
turbulence on the propagation properties of such laser arrays has been studied
in great detail. Our main results show that the atmospheric turbulence may
result in the prohibition of the formation of the optical vortex or the
disappearance of the formed optical vortex, which are very different from that
in the free space. The formed optical vortex with the higher topological charge
may propagate over a much longer distance in the moderate or weak turbulent
atmosphere. After the sufficient long-distance atmospheric propagation, all the
output beams (even with initially different phase distributions) finally lose
the vortex property and gradually become the Gaussian-shaped beams, and in this
case the output beams actually become incoherent light fields due to the
decoherence effect of the turbulent atmosphere.
