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In the modeling of vegetated flows an efficient approach is to solve the Double Averaged Navier Stokes (DANS) equations, which are obtained from the spatial and temporal averaging of the Navier Stokes equations. The resistance effects of vegetation are modeled by a drag force density term with an empirical bulk drag coefficient, as well as by turbulence terms characterized by a length scale parameter. These empirical parameters are dependent on the areal density of vegetation and the spatial distribution pattern of vegetation elements and have seldom been studied. In this work the effect of spatial distribution of vegetation elements on the bulk drag coefficient is investigated by computing explicitly the flows around the vegetation elements. The results show that the bulk drag coefficient increases with the longitudinal vegetation element spacing, decreases with the lateral vegetation element spacing and can have multiple values for a given areal density of vegetation. In the DANS model the vegetation induced turbulence is simulated by a novel k-type model embracing an empirical length scale parameter. The length scale parameters are calibrated against previous experiments and a new set of experiments with high areal density of vegetation. The DANS model is subsequently verified by two cases with the same vegetation density and different distribution patterns.

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