Modeling turbulent stream flows over rough permeable beds

In steep streams, turbulent flows run over coarse sediments that are similar in size to flow depth. Under these conditions, a significant part of the flow may seep through the permeable bed. Based on experimental data, this paper presents a model able to reproduce the vertical structure of flows over rough permeable beds in low relative submergence conditions. Experiments were performed on open-channel flows passing over tilted coarse-grained beds with slopes within the 0.5% – 4% range. Fluid velocities were measured by Particle Image Velocimetry (PIV) and a technique called Refractive Index-Matched Scanning (RIMS), allowing the interior of the bed to be examined. By applying the double averaging methodology, porosity and mean velocity, as well as turbulent and dispersive stresses profiles were collected from the subsurface to the free surface. A turbulent boundary layer over the rough bed was observed while experiments were run at intermediate Reynolds numbers, i.e. Re = O(1000). Under these flow conditions, viscosity played a non-negligible role through the van Driest damping effect. Based on the Prandtl mixing length theory, we propose a model for the turbulent stress that takes into account the continuous porosity profile, damping and dispersive effects. Finally, we show a good agreement between the model and classic flow resistance laws employed for river studies. Our model contrasts with existing boundary-layer models which generally assume a discontinuous porosity profile at bed interface, whether the bed is permeable or impermeable.