Longitudinal Dispersion in Straight Open Channels: Anomalous Breakthrough Curves and First-Order Analytical Solution for the Depth-Averaged Concentration

Abstract

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.

Theoretical Investigation of Equilibrium Dynamics in Braided Gravel Beds for the Preservation of a Sustainable Fluvial Environment

“…Then, we solved Equation ( 27) by particle-tracking (e.g., [58][59][60][61]) for s (x, y, t) = 0 and:…”

A Theoretical Study about Ergodicity Issues in Predicting Contaminant Plume Evolution in Aquifers

“…In terms of position and dimensions, the discussion is based on centroid and central inertia moments, as well as on the conditions under which they can be considered as equivalent to same-order single-particle statistical moments; in terms of point concentrations, the discussion is based on concentration ensemble mean, variance and coefficient of variation (which in turn involve the single-particle moments as well as the statistics of the barycenter of mass) and the conditions under which the Gaussian ensemble mean for point instantaneous mass injection can be representative of the actual distribution. The mathematical treatment, which also hinges on previous author's results, makes use of both Lagrangian (e.g., [8][9][10][11][12][13]) and Eulerian (e.g., [14][15][16]) framework for tracer transport in heterogeneous flow fields.…”