The analytical expressions for the mean-squared beam width and the far-field divergence angle of radial Gaussian array beams in atmospheric turbulence are derived. The influence of turbulence on the spreading and directionality is studied in detail. It is shown that for the coherent combination, the radial Gaussian array beams with smaller beam number N and larger radial radius r0 are less affected by the turbulence. The spreading of radial Gaussian array beams for the coherent combination is smaller than that for the incoherent case. However, the spreading of radial Gaussian array beams for the coherent combination is more affected by turbulence than that for the incoherent case. Specially, the mean-squared beam width in the far-field for the coherent combination is the same as that for the incoherent case when N is small enough or r0 is large enough. On the other hand, the condition under which radial Gaussian array beams for both coherent and incoherent combinations have the same far-field divergence angle as a single Gaussian beam is also given. The main results are interpreted physically.