Effect of nonlocal transverse mixing on river flows dispersion: A numerical study

Abstract

[1] A series of Lagrangian numerical simulations is performed to examine the dispersion process in open channel flows and to explain through a simple conceptual model its systematic deviations from the ideal long-term one-dimensional regime even in the case of straight axis and fixed impervious bed. The starting point is represented by a suitably depth-averaged transport equation, with generally nonlocal turbulent mixing, solved in terms of particles trajectories and their first-and second-order moments. Input data refer to six rivers of southern Italy, for which the irregular section morphology is known from a field survey. As the governing equation predicts, and according to experimental observations, in the case of variable cross-sectional diffusion the tracer cloud exhibits a permanent and asymmetric peripheral drift toward the shallow boundary zones, with a remarkable deceleration along the main flow direction. Longitudinal inertia moments tend to become linear after a period equal to twice the single river diffusive time and sometimes show an early anomalous change of slope. Transverse inertia moments experience an initial very fast increment as compared to the theoretical value corresponding to the uniform transverse concentration and, after a peak, tend to stabilize about a smaller constant. Centrifugal moments remain, in any case, relatively limited, indicating that longitudinal and transverse axes practically identify with the plume principal directions, no matter how irregular and asymmetric the river section is.

On the exact analytical solution for the spatial moments of the cross‐sectional average concentration in open channel flows

“…Thus, the only restriction for the application of those formulas to any type of real river and any type of real section resides in the possibility to resort to a two-dimensional transport equation like (7). As shown in a previous paper [Pannone, 2010], the analytical/physical requirement enabling that application concerns the relative magnitude of the transverse depth gradient:…”

“…recommendable for practical use. A previous author's numerical study [Pannone, 2010] had illustrated how, in presence of variable-depth cross sections, the corresponding nonuniform mixing coefficients trigger off an anomalous dispersion process characterized by pronounced plume asymmetries, highly concentrated side solute pockets, and strongly nonlinear center of mass trajectories.…”

Predictability of tracer dilution in large open channel flows: Analytical solution for the coefficient of variation of the depth‐averaged concentration

“…Note that in (42) u à represents the single grid-element velocity u multiplied by the ratio of the local depth to the depth of the rectangular equivalent cross section in order to meet the continuity condition in the twodimensional numerical experiment [e.g., Pannone, 2010b]. Of course, in case of rectangular cross sections and transversally uniform depth, u à 5 u. X and Y represent the components of the particle position vector along the longitudinal and the transverse axis, respectively.…”

“…Many classical and more recent studies have provided a variety of closed-form solutions for that fundamental parameter, resorting to different theoretical approaches or experimental methods, in both transient and steady state conditions [e.g., Fischer et al, 1979;Seo and Cheong, 1998;Deng et al, 2001;Kashefipour and Falconer, 2002;Seo and Baek, 2004;Pannone, 2010aPannone, , 2012aPannone, , 2012b. However, as shown in previous author's works [Pannone, 2010b[Pannone, , 2012b, and in contrast with what predicted by the asymptotic Taylor's [1954] theory, both the peculiar initial conditions and the pronounced irregularity of the cross section, often associated with a marked nonuniformity of the transverse mixing, can lead to the appearance of permanent side solute pockets or, at best, to long transients and persistent average concentration asymmetries. Then, the availability of an analytical tool enabling the estimation of the point-concentration values is crucial in the handling of the river-flow pollution events, particularly when stream dimension and heterogeneities of the velocity distribution make the so-called near and intermediate fields (the first stages of the fluvial dispersion-dilution process) a very large space-time domain.…”

An Analytical Model of Fickian and Non-Fickian Dispersion in Evolving-Scale Log-Conductivity Distributions

“…The crucial role of local dispersion (sometimes simply named 'diffusion') in solute macro-dispersion and dilution was already explored in the context of subsurface flow and transport by Pannone and Kitanidis [25] and in the context of river-flow and transport by Pannone [26,27]. Overall, these studies showed that, in the case of heterogeneous structures characterized by short-range correlations, macro-dispersion and dilution are singularly driven by the interplay of advective heterogeneities and diffusive-like mechanisms.…”