Longitudinal dispersion in straight open channels: Anomalous breakthrough curves and first-order analytical solution for the depth-averaged concentration

A first-order analytical solution is proposed for the actual depth-averaged concentration of tracers in shallow river flows in the presence of large Peclet numbers (defined as the ratio of section-averaged velocity times channel width to turbulent diffusion coefficient). The solution shows how complete transverse mixing is never achieved due to the typical shape of the velocity and diffusion coefficient profile, which alternatively tend-depending on the downstream location of the cross-section-to concentrate the mass at the centre or at the boundaries of the cross-section itself. The first-order analytical solution proves to be consistent with the results of Lagrangian numerical simulations based on real-field input data, which show how the solute mass breakthrough curves always exhibit anomalous behaviour and a considerable and persistent delay when compared with those that are analytically obtained by assuming a truly one-dimensional process.