Stochastic numerical analysis of anomalous longitudinal dispersion and dilution in shallow decelerating stream flows

The paper deals with the numerical analysis of solute dispersion and dilution within shallow stream flows which are characterized by a low gradient and undergo a downstream deceleration, near the confluence into large reservoirs or upstream from fluvial barrages. The main purpose of the study consists in investigating the effect that the size and the slope of the channel induce on solute transport in the presence of backwaters. The analysis, performed by a numerical stochastic Lagrangian approach, detects a characteristic travel time beyond which the longitudinal hydrodynamic dispersion, jointly with dilution, undergoes a drastic decline. One of the key results of the simulations is indeed represented by the possibility to estimate the large-time section-averaged concentration resorting to the classic Gaussian distribution characterized by the actual first- and second-order particle moments and, therefore, by increasing and asymptotically constant values. In addition, the assessment of dilution at cloud scale, performed through the entropic evaluation of the total volume occupied by the solute and a closed-form expression of the geometric mean of the reactor ratio, reveals that, after a transient characterized by the earlier tendency to the cross-sectional mixing, the backwater flows induce a global re-densification of the cloud and a permanent transverse non-uniformity.