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The sand dunes are typical bed forms of natural alluvial rivers. In this article, a vertical 2-D Reynolds stress model is established for the simulation of turbulent flows around sand dunes, and water-sand boundary conditions are set with particular attention. By numerical simulations, the following conclusions can be drawn. (1) The flow resistance in rivers with sand dunes could be divided into the sand-grain resistance and the sand dune resistance, and the sand-grain resistance coefficient mainly depends on Reynolds number, relative sand grain roughness and sand dune steepness. This coefficient in rivers with sand dunes would be larger than that calculated in a flat riverbed, and the steeper the sand dunes, the larger the sand-grain resistance coefficient. (2) The sand dune resistance coefficient mainly depends on the relative sand dune height and sand dune steepness, the steeper the sand dunes, the larger the sand dune resistance coefficient. (3) For the flat riverbed, the turbulent eddy viscosity coefficient and the sediment diffusion coefficient are approximately identical, but for the sand dune riverbed, in the vertical position, where the sediment diffusion coefficient reaches its maximum, it would be higher than the turbulent eddy viscosity coefficient.