This is the second paper in a series where we study the influence of transport processes on the chemical evolution of protoplanetary disks. Our analysis is based on a flared alpha-model of the DM Tau system, coupled to a large gas-grain chemical network. To account for production of complex molecules, the chemical network is supplied with an extended set of surface reactions and photo-processes in ice mantles. Our disk model covers a wide range of radii, 10-800 AU (from a Jovian planet-forming zone to the outer disk edge). Turbulent transport of gases and ices is implicitly modeled in full 2D along with the time-dependent chemistry. Two regimes are considered, with high and low efficiency of turbulent mixing. The results of the chemical model with suppressed turbulent diffusion are close to those from the laminar model, but not completely. A simple analysis for the laminar chemical model to highlight potential sensitivity of a molecule to transport processes is performed. It is shown that the higher the ratio of the characteristic chemical timescale to the turbulent transport timescale for a given molecule, the higher the probability that its column density will be affected by diffusion. We find that turbulent transport enhances abundances and column densities of many gas-phase species and ices, particularly, complex ones. For such species a chemical steady-state is not reached due to long timescales associated with evaporation and surface photoprocessing and recombination. In contrast, simple radicals and molecular ions, which chemical evolution is fast and proceeds solely in the gas phase, are not much affected by dynamics. All molecules are divided into three groups according to the sensitivity of their column densities to the turbulent diffusion. [Abridged]Comment: 42 pages, 13 figures, 16 tables, accepted for publication in ApJS
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