Longitudinal scattering coefficient obtained by hydroacoustic measurement and by conservative tracer

The objective of the present work was to determine the value of the longitudinal dispersion coefficient (DL) of the Chicamtoltina stream (Alta Gracia) by means of two different techniques, in order to compare the values obtained. The first technique consisted of applying a developed formula that includes a detailed description of hydrodynamic parameters obtained by gauging with a hydroacoustic instrument, while the second technique consisted of injecting a conservative tracer, using the same approach as the non-ideal chemical reactor theory of flow with dispersion. This work was carried out at low flow conditions (dry period) and at high flow conditions (wet period). It was found that, either for high flow or low flow, the values of the dispersion coefficient obtained by both techniques have good agreement, fitting better in the dry period than in the wet period. Due to the fact that frequent gauging campaigns are carried out in this stream, it is concluded that with similar flow characteristics and morphology of the section, the gauging data can be used to determine the DL coefficient, in order to incorporate reliable data that can be applied to pollutant transport models.

Effect of cadmium sorption by river sediments on longitudinal dispersion

This paper concerns the cadmium sorptive effects by river bed sediments on longitudinal dispersion coefficient in an open-channel flow via experimental and numerical study. For this purpose, a circular flume was used with mean diameter of 1.6 m and a width of 0.2 m. The adsorbing bed was considered as a thin layer of the sediment particles with mean diameter of 0.53 mm and three sediment concentrations of 3, 12, and 20 gr/lit. To determine the sorption parameters of the sediments, some experiments were conducted with three cadmium concentrations of 150, 460, and 770 ppb. Then, the dispersion experiments were carried out with and without the bed sediments with the same cadmium concentration as the sorption experiments. A numerical model was then developed to solve the advection-dispersion equation with considering the sorption term by river bed sediments. The longitudinal dispersion coefficients were estimated by comparing the experimental and numerical breakthrough curves. The results showed that, with increasing the sediment concentrations, the sediment sorption rate increased and the longitudinal dispersion coefficient decreased by about 38, 36 and 33 percent, respectively, for cadmium concentrations of 150, 460 and 770 ppb. In addition, by increasing the cadmium concentrations, the changes in the longitudinal dispersion coefficient are decreased. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion as a function of the new parameter of sorption ratio. From a practical point of view, the results of this study demonstrated that, at the presence of riverbed sediment, the cadmium is longitudinally dispersed with more delay in comparison with no sediment at the river bed.

Fate of turbid glacial inflows in a hydroelectric reservoir

Turbidity from glacial meltwater limits light penetration with potential ecological consequences. Using profiles of temperature, conductivity, and turbidity, we examine the physical processes driving changes in the epilimnetic turbidity of Carpenter Reservoir, a long and narrow, glacier-fed reservoir in southwest British Columbia, Canada. Following the onset of permanent summer stratification, the relatively dense inflows plunged into the hypolimnion, and despite the high glacial load entering the reservoir, the epilimnion cleared due to particle settling. Using a one-dimensional (longitudinal) diffusion equation for a decaying substance to describe the variation in epilimnetic turbidity, we obtain two nondimensional parameters: the epilimnetic inflow parameter, $$\mathcal {I}$$ I , a measure of the turbidity flux into the epilimnion; and the dispersion parameter, $${\mathcal {D}}$$ D , a measure of longitudinal dispersion. In the case of Carpenter Reservoir: $$\mathcal {I}\ll 1$$ I ≪ 1 , indicating that turbidity declines over the summer; and $${\mathcal {D}}\ll 1$$ D ≪ 1 , indicating a strong gradient in turbidity along the epilimnion. Using our theoretical formulation of epilimnetic turbidity variations in conjunction with monthly field surveys, we compute the particle settling velocity ($${\sim}{0.25}\,{\hbox {m}\,\hbox {d}^{-1}}$$ ∼ 0.25 m d - 1 ), the longitudinal dispersion coefficient (50–70 $${\hbox {m}^{2}\,\hbox {s}^{-1}}$$ m 2 s - 1 ), and the flux of turbid water into the epilimnion ($${\sim }1{\%}$$ ∼ 1 % of the total inflow). Our approach is applicable to other reservoirs and can be used to investigate changes in turbidity in response to changes in $$\mathcal {I}$$ I and $${\mathcal {D}}$$ D .

Experimental and numerical study of bed roughness effect on longitudinal dispersion

The effects of bed roughness on the longitudinal dispersion coefficient (DL) were experimentally and numerically investigated in the present study. The tracer experiments were first carried out in a circular flume with a diameter of 1.6 m over both smooth and rough beds (coarse sand) with four sizes (ks = d65) of 1.04, 2.09, 3.01, and 4.24 mm. In addition, the one-dimensional advection-dispersion equation was numerically solved. The longitudinal dispersion coefficient was calculated by comparing the numerical and experimental breakthrough curves. The results showed that by increasing the bed roughness height (from zero to 4.24 mm), the longitudinal dispersion coefficient increased by 34%. In addition, the longitudinal dispersivity (λ = DL/V) increased with increasing relative roughness (ks/h), so that the range of longitudinal dispersivities in smooth bed experiments were 0.037–0.049 m and for rough bed (ks = 4.24 mm) were 0.07–0.084 m. In other words, with increasing the bed roughness height from zero (smooth bed) to 4.24 mm, the longitudinal dispersivities increased from 0.037 to 0.077 m, indicating an increase of about 108%. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion (DL/(Vh)) as a function of relative roughness (ks/h). It can be concluded that taking into consideration bed roughness as the driving force of shear dispersion would improve predictive equations of the longitudinal dispersion in the rivers. Since the bottom of all natural rivers has roughness elements with different sizes, the results of this study will definitely be useful in estimating the longitudinal dispersion coefficient in natural rivers and quantifying the effect of roughness in the longitudinal dispersion coefficient equations.

Evaluating longitudinal dispersion of scalars in rural channels of agro-urban environments

In agro-urban environments, the water resource conveyed by rural channels is susceptible to a gradual impoverishment due to the continuous combined sewer overflow release, constituting a pending and urgent issue for water management companies and the entire community. Reliable one-dimensional longitudinal dispersion coefficients D are required to model and study the hydrodynamics and water quality patterns at the scale of rural channel networks. Empirical formulas are usually adopted to estimate D but the accuracy in the prediction could be questionable. In order to identify which are the most suitable formulas to determine D in rural channels, field tracer measurements were carried out in three rural channels with typical geometry and configuration. The obtained D values were then compared with the most commonly used predicting formulas that the literature provides. The accuracy of the predictors was further checked by simulating different flow rates inside the tested channels by using a one-dimensional hydraulic model. Starting from the obtained results, indications and guidelines to choose the most suitable formulas to predict D in rural channels were provided. These indications should be followed when developing realistic quality models in the agro-urban environments, especially in those cases where direct measurements of the longitudinal dispersion coefficient D are not available.

Experimental and Numerical Investigation of Effect of Cadmium Sorption by River Sediments on Longitudinal Dispersion

This paper concerns the cadmium sorptive effects by river bed sediments on longitudinal coefficient in an open-channel flow via experimental and numerical study. For this purpose, a circular flume was used with mean diameter of 1.6 m and a width of 0.2 m. The adsorbing bed was considered as a thin layer of the sediment particles with mean diameter of 0.5 mm and three sediment concentrations of 3, 12, and 20 gr/lit. To determine the sorption parameters of the sediments, some experiments were conducted with three cadmium concentrations of 150, 460, and 770 ppb. Then, the dispersion experiments were carried out with and without the bed sediments. To solve the advection-dispersion equation with considering the sorption term by river bed sediments, a numerical model was then developed. The longitudinal dispersion coefficients were estimated by comparing the experimental and numerical breakthrough curves. The results showed that, with increasing the sediment concentrations, the sediment sorption rate increased and the longitudinal dispersion coefficient decreased by about 38, 36 and 33 percent, respectively, for cadmium concentrations of 150, 460 and 770 ppb. In addition, by increasing the cadmium concentrations, the changes in the longitudinal dispersion coefficient are decreased. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion as a function of the new parameter of sorption ratio. From a practical point of view, the results of this study demonstrated that, at the presence of sediment, the cadmium is longitudinally dispersed with more delay in comparison with no sediment at the river bed.

Reliability-based design and implementation of crow search algorithm for longitudinal dispersion coefficient estimation in rivers

The longitudinal dispersion coefficient (LDC) of river pollutants is considered as one of the prominent water quality parameters. In this regard, numerous research studies have been conducted in recent years, and various equations have been extracted based on hydrodynamic and geometric elements. LDC’s estimated values obtained using different equations reveal a significant uncertainty due to this phenomenon’s complexity. In the present study, the crow search algorithm (CSA) is applied to increase the equation’s precision by employing evolutionary polynomial regression (EPR) to model an extensive amount of geometrical and hydraulic data. The results indicate that the CSA improves the performance of EPR in terms of R2 (0.8), Willmott’s index of agreement (0.93), Nash–Sutcliffe efficiency (0.77), and overall index (0.84). In addition, the reliability analysis of the proposed equation (i.e., CSA) reduced the failure probability (Pf) when the value of the failure state containing 50 to 600 m2/s is increasing for the Pf determination using the Monte Carlo simulation. The best-fitted function for correct failure probability prediction was the power with R2 = 0.98 compared with linear and exponential functions.