Estimating longitudinal dispersion coefficients in natural channels

A new empirical formula is developed for estimating the longitudinal dispersion coefficient. Velocity profiles are computed from the momentum equation as presented by Shiono and Knight (1991), and the dispersion coefficient is computed from the velocity profiles using the theory of shear dispersion (Taylor 1953, Fischer et al. 1979). To simplify the application, results of the numerical integration are expressed in terms of the aspect ratio of the channel, the friction factor, the dimensionless eddy viscosity, and the secondary flow coefficient using multiple regression. For laboratory data, 83.3% of the empirical estimates from the initial formula fall within 50% of values from tracer measurements. After adjustment of the initial formula, the second formula predicts the data of Nordin and Sabol (1974) as well as the formula of Wang and Huai (2016). For example, both the proposed formula and the formula of Wang and Huai (2016) have mean and median values of the discrepancy ratio of −0.12 and standard deviation less than 0.5