Estimation of Transverse Mixing Coefficient in Straight and Meandering Streams

Abstract

Transverse mixing coefficient (TMC) is one of the key factors in the modelling of lateral dispersion of pollutants. Several researchers have attempted to estimate this coefficient using various models. However, robust equations that can accurately estimate lateral mixing in both straight and meandering streams are still required. In this study, novel formulae were developed using the hydraulic and geometric parameters of rivers. The multiple linear regression (MLR), genetic programming based symbolic regression (GPSR) and dimensionless parameters were used for this purpose. Two extensive data sets including data from straight channels/streams and meandering ones were employed to develop the formulae. The main advantage of the developed formula for meandering streams is proper consideration of the effects of aspect ratio, friction, and sinuosity. The formulae performances were then compared quantitatively with those of existing ones using accuracy metrics such as RMSE (Root Mean Square Error). The results illustrated that the proposed formulae outperform others in terms of accuracy and can be used for estimating TMC in straight and meandering streams. In addition, the comparison of MLR and GPSR models showed that the latter is marginally more accurate than MLR specially in meandering streams. However, the MLR models presented a more justifiable relationship between the TMC and governing dimensionless parameters. The main advantages of the presented formulae are that they are more accurate than previous models, can be used in both meandering and straight streams; and can be easily implemented in numerical models to estimate the pollutant concentration and mixing length

Improvements in the Explicit Estimation of Pollutant Dispersion Coefficient in Rivers by Subset Selection of Maximum Dissimilarity Hybridized With ANFIS-Firefly Algorithm (FFA)

“…The diffusion coefficient is generally referred to the longitudinal dispersion coefficient [6], [8]. The injected pollutants are dispersed by advection and dispersion processes in longitudinal, vertical, and transverse directions [9], [10]. The longitudinal dispersion process becomes the main mechanism, when the mixing process in the lateral direction is fully developed [11], [12].…”

“…hu dy dy dy (2) where A is the area of river cross-section, B is the river width, h is the flow depth, u is the differences of the depth-averaged flow velocity at specified local y from average velocity over the cross-section of river, y is the location in the lateral direction, and ε t is the local transverse mixing coefficient [9]. Longitudinal dispersion coefficient (K x ) has a significant effect on contaminants and mass transport in large rives [18].…”

Transverse Mixing in Rivers With Longitudinally Varied Morphology

“…The ability of equations recently published by Aghababaei et al (2017), Deng et al (2001), Huai et al (2018), and Jeon et al (2007) to predict the measured transverse mixing coefficients is tested here. Four equations GOND ET AL.…”

“…The parameter is the channel sinuosity (the ratio between the curvilinear length and the Euclidean distance between two points of the flow axis), sometimes replaced by (Fischer, 1969) or (Yotsukura & Sayre, 1976) with the curvature radius of the channel in the case of a single bend. Along with the aspect ratio , the sinuosity reflects the mixing due to dispersion by secondary currents in curved channels (Aghababaei et al., 2017; Huai et al., 2018; Jeon et al., 2007), while the so‐called friction ratio , sometimes replaced by the friction coefficient , reflects the mixing due to turbulent diffusion (Webel & Schatzmann, 1984).…”

Drought Frequency Analysis Based on the Development of a Two-Variate Standardized Index (Rainfall-Runoff)

“…As a significant coefficient to find a statistical relationship between two variables, the correlation coefficient has been widely applied in the literature [18,19]. In this regard, several methods such as Pearson's classical correlation coefficient, Spearman's correlation coefficient, Kendall's tau, chi-plot, k-plot, and rank scatter plot are commonly used to assess the dependency between two random variables.…”