Estimation of longitudinal dispersion coefficient in rivers

• 116 sets of measured data for rivers in U.S. and UK have been collected for analysis.
• The adaptations of frequently-used empirical equations were compared.
• An empirical equation with a higher precision was presented.

The longitudinal dispersion coefficient is a crucial parameter for 1D water quality analyzing in natural rivers, and different types of empirical equations have been presented in the literature. To evaluate the precision of those commonly used equations, 116 sets of measured data for rivers in U.S. and UK have been collected for comparison. Firstly, the precisions of selected ten empirical equations under different aspect ratio (water surface width B/water depth H) have been compared, and calculation shows that most of the equations have underestimated the longitudinal dispersion when 20 < B/H < 100, in which most of the natural rivers located. The regression analysis on the collected data sets proved that the product of water depth H and the cross-sectional averaged velocity U has a higher linear correlation with the longitudinal dispersion coefficient than the product of H and shear velocity u∗, and then a new expression of longitudinal dispersion coefficient, which is a combination of the product of HU and other two nondimensional hydraulic and geometric parameters, was deduced and the exponents were determined by the regression analysis. The comparison between the measured data and the predicted results shows that the presented equation has the highest precision for the studied natural rivers. To further evaluate the precision of the empirical formulae to artificial open channels, comparison was made between laboratory measuring data and empirical equation prediction, and the results have shown that the newly presented model is effective at predicting longitudinal dispersion in trapezoidal artificial channels too.