Abstract
Accurate prediction of pollutant concentrations in a river course is of great importance in environmental management. Mathematical dispersion models are often used to predict the spatial distribution of substances to help achieve these objectives. In practice, these models use a dispersion coefficient as a calibration parameter that is calculated through either expensive field tracer experiments or through empirical equations available in the scientific literature. The latter are based on reach-averaged values obtained from laboratory flumes or simple river reaches, which often show great variability when applied to natural streams. These equations cannot directly account for mixing that relates specifically to spatial fluctuations of channel geometry and complex bed morphology. This study isolated the influence of mixing related to bed morphology and presented a means of calculating a predictive longitudinal mixing equation that directly accounted for pool-riffle sequences. As an example, a predictive equation was developed by means of a three-dimensional numerical model based on synthetically generated pool-riffle bathymetries. The predictive equation was validated with numerical experiments and field tracer studies. The resulting equation was shown to more accurately represent mixing across complex morphology than those relations selected from the literature.
Highlights
Understanding the fate and transport of introduced pollutants and substances within river courses is relevant for public health, ecological diversity, and the administration of water resources [1,2,3,4].Fundamental to this understanding is the accurate prediction of substance concentrations and their distribution, owing to mechanisms such as advection, molecular diffusion, and dispersion, where the former is the most dominant process in natural rivers [5]
Prediction of longitudinal mixing is complicated in natural rivers as the channel morphology increases in complexity [11,12,13,14,15,16]
A straight-channel bathymetry was studied in order to observe the effect of the vertical convergence and horizontal divergence of flow characteristics of the pool-riffle macroform on the dispersion coefficient
Summary
Understanding the fate and transport of introduced pollutants and substances within river courses is relevant for public health, ecological diversity, and the administration of water resources [1,2,3,4]. Prediction of longitudinal mixing is complicated in natural rivers as the channel morphology increases in complexity (e.g., planform curvature, bed irregularity, variable roughness provided by macroforms, substrate, and vegetation) [11,12,13,14,15,16] Under such circumstances the inertial terms in the hydrodynamic equation become increasingly important for mixing and pollutant transport. To obtain these estimates of reach-averaged dispersion coefficients, many authors have carried out tracer studies [26,33,36,37,38,39,40,41] Many of these empirical models have been validated in the laboratory or simple stream reaches, whereas natural alluvial rivers present variations in planform and bed topography, which deviate from a plane configuration [4] and rarely satisfy the implicit assumptions (Table 1). Five field tracer studies were used to validate the predictive equation
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