Studies in open-channel flows are very interesting because they allow to reach rather high Reynolds number situations with rather low velocities, these low velocities being appropriate for performing flow visualisations as well as detailed laser doppler velocimetry or particle image velocimetry measurements. The lecture will be organized in two parts.

In the first part, the development region of turbulent pipe, duct or open channel flows will be analyzed in detail. This development region is characterized by a regular acceleration of the flow, as a result of the progressive thickening of the boundary layers on the walls. It seems that there has been no systematic study to quantify and analyze in detail the properties of this region. In particular, if the hydraulic diameter D_h has long been recognized as being an important parameter to normalize the longitudinal distance from the inlet, X, when the cross section is not circular, there has been no proposal to take into account the influence of the Reynolds number when the flow is turbulent. Also, there has been no systematic study of the relative development properties of circular pipes, ducts of square or rectangular cross-sections and open channel flows (of variable water depth $h$). The results we obtained from a combined experimental/numerical investigation display the properties of the development regions for these three types of flows. They mostly show that circular pipes develop at the same rate as ducts of square or rectangular cross-sections and open-channel flows, these three types of flows attaining almost the same asymptotic level in terms of the centreline velocity U_e normalized by the bulk velocity U_b. The acceleration U_e/U_b then appears to be a unique function of the quantity delta_1/D_h (where delta_1 is the boundary layer displacement thickness for the considered case, which depends on both the value of X and the value of U_b). Other characteristic properties of the flow (such as the wall friction coefficient or the entrance region length) are then inferred in a rather straightforward way.

In the second part, two environmental problems studied with the help of the open-channel flow recently built at IRPHE will be considered. The first one is related to sediment dynamics. Indeed, pollutants and suspended matters of a river generally accumulate into the sedimentary column. Once deposited, they are submitted to autoconsolidation processes, ageing and burying, leading to an increase of their erosion resistance. Pollutant fluxes can be related to sedimentary fluxes, the erosion of which is determined by threshold laws. Artificial erosion expriments are thus performed in the open-channel flow with natural cored sediments and the critical shear stresses are measured, together with the matter granulometry and the core porosity. To develop a model for these critical shear stresses, both the sedimentary layer and the cohesive particule (clays) interactions, particularly the surface Van der Waals force, must be taken account. The model is then applied to the experimental conditions and good agreement with measurements if obtained. Fianlly, account of autoconsolidation processes is also suggested, which allows to derive a Mohr-Coulomb.s like diagram dedicated to cohesive sediment erosion.

The second problem concerns aerosol dry deposition on vegetated canopies. To develop a new modelling approach of this problem, the flow characteristic properties within the canopy must first be determined and parametrized. This was performed in the open-channel flow, using artificial small-scale model trees, and results were compared with published data obtained in real canopies. Then, a theoretical framework, based on the concept of weighting functions for performing space and time averages of the governing equations, is developed. This provides a new closure of the deposition term which involves an up-scaling procedure based on the statistical distribution of the canopy properties. This modelling approach is applied in a simple configuration, in which it takes into account the canopy structural and morphological properties, the main characteristics of the turbulent flow and the aerosol properties. The considered deposition mechanisms are Brownian diffusion, interception, inertial and turbulent impaction, and gravitational settling. Validations of the model are made with existing measurement campaigns, both on isolated coniferous branches and on entire canopies of different roughness, such as grass and forest.