Assessing flow resistance law in vegetated channels by dimensional analysis and self-similarity

In this paper experimental data collected by Kouwen et al., Wilson and Horrit, Raffaelli et al. and Carollo et al., using straight flumes having a bed covered by grass-like vegetation with different stem concentrations, were used to analyze flow resistance for flexible submerged elements. At first, the dimensional analysis and the incomplete self-similarity hypothesis was applied to deduce the flow velocity distribution and the resulting theoretical expression of the Darcy-Weisbach friction factor. Then, a relationship between the Γ function of the velocity profile and the biomechanical characteristics of vegetation, the channel slope, the Reynolds number and the flow Froude number was empirically deduced by the available measurements. This relationship was established distinguishing between the low stem concentration values and the highest values for which a quasi-smooth skimming flow occurs. Finally, the analysis showed that, in comparison with previous results, a more accurate Darcy-Weisbach friction factor estimate can be obtained by the theoretical approach based on a power-velocity profile.