Velocity Profiles in Gravel Beds Based on Refractive Index Matching Experiments

Abstract

The space-and time-averaged velocity profiles in gravel beds show some features that differentiates them from that established in smooth beds, but the obstruction posed by the gravel hampers the experimental measurements below the sediments. To overcome such difficulties, we coupled particle image velocimetry (PIV) with refractive index matching (RIM) by means of substituting the gravel with hydrogel spheres. We applied a superposition of models on the experimental velocity profile: the Darcy, the mixing, the logarithmic, and the wake law models. The resulting analytical profile is adherent to the experimental data in all the regions of the flow, from the bottom to the free surface. After including a second data set from literature, we carried out the dimensional analyses on the parameters in the profile, defining them as functions of the general characteristics of the flow and of the bed. In particular, the position of the inflection point, and thus the relative contribution of the mixing and the logarithmic layers on the overall profile, were found to be related to the permeability Reynolds number.