A Semi-Analytical Model for the Hydraulic Resistance Due to Macro-Roughnesses of Varying Shapes and Densities

A friction model resulting from investigations into macro-roughness elements in fishways has been compared with a broad range of studies in the literature under very different bed configurations. In the context of flood modelling or aquatic habitats, the aim of the study is to show that the formulation is applicable to both emergent or submerged obstacles with either low or high obstacle concentrations. In the emergent case, the model takes into account free surface variations at large Froude numbers. In the submerged case, a vegetation model based on the double-averaging concept is used with a specific turbulence closure model. Calculation of the flow in the roughness elements gives the total hydraulic resistance uniquely as a function of the obstacles’ drag coefficient. The results show that the model is highly robust for all the rough beds tested. The averaged accuracy of the model is about 20% for the discharge calculation. In particular, we obtain the known values for the limiting cases of low confinement, as in the case of sandy beds