Simulation of Accelerated Subcritical Flow Profiles in an Open Channel with Emergent Rigid Vegetation

Even though both fluid mechanics and numerical studies have considerably progressed in the past decades, experimental knowledge remains an important tool for studying the resistance to flow in fluid media where a complex environment dominates the flow pattern. After a comprehensive review of the recent literature on the drag coefficient in open channels with emergent rigid vegetation, this paper presents the results related to 29 experimental accelerated subcritical flow profiles (i.e., M2 type) that were observed in flume experiments with emergent stems in a square arrangement at the University of Calabria (Italy). First of all, we used some of the literature formulas for the drag coefficient, concluding that they were unsatisfactory, probably because of their derivation for uniform or quasi-uniform flow conditions. Then, we tested a recently proposed approach, but when we plotted the drag coefficient versus the stem Reynolds number, the calculated drag coefficients showed an inconclusive behavior to interpret. Thus, we proposed a new approach that considers the calibration of the Manning coefficient for the simulation of the free surface profile, and then the evaluation of the drag coefficients based on the fundamental fluid mechanics equations. With the help of classical dimensional analysis, a regression equation was found to estimate the drag coefficients by means of non-dimensional parameters, which include vegetation density, stem Reynolds number and flow Reynolds number computed using the flow depth as characteristic length. This equation was used to simulate all the 26 observed profiles and, also, 4 experimental literature profiles, and the results were good. The regression equation could be used to estimate the drag coefficient for the M2 profiles in channels with squared stem arrangements, within the range of vegetation densities, flow Reynolds numbers and stem Reynolds numbers of the present study. However, in the case of the three profiles observed by the authors for staggered arrangement, the regression equation gives significantly underestimated flow depths.