Experimental and numerical study of bed roughness effect on longitudinal dispersion

The effects of bed roughness on the longitudinal dispersion coefficient (D-L) 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 (k(s) = d(65)) 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 (lambda = D-L/V) increased with increasing relative roughness (k(s)/h), so that the range of longitudinal dispersivities in smooth bed experiments were 0.037-0.049 m and for rough bed (k(s) = 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 (D-L/(Vh)) as a function of relative roughness (k(s)/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.