Theoretical analysis of pollutant mixing zone considering lateral distribution of flow velocity and diffusion coefficient

Abstract

Theoretical formulae have shown significant advantages in describing the characteristic geometric scales of the pollutant mixing zone (PMZ) formed by offshore pollutant discharged by a single general form. They, however, fail to predict the influence of the lateral inhomogeneity of the river flow because constant flow velocity and the lateral diffusion coefficient are assumed during the derivation. The realistic flow velocity in a river is fitted by an exponential law in this study and the lateral diffusion coefficient is proposed to have the same form. Similar idea has been used in previous studies on the vertical dispersion of scalar in the lower atmosphere. Pollutant discharged from a steady onshore point source into a wide straight open channel is examined to characterize the concentration taking into consideration of these lateral variations. Theoretical formulae describing the maximum length, maximum width and its corresponding longitudinal position, as well as the area of the PMZ are derived. A non-dimensional standard curve equation for the isoconcentration boundary of PMZ is also obtained. The results show that the shape of the dimensionless standard curve of PMZ depends only on the exponential constants in the exponential laws. The exponential profiles that fit the near-shore velocity give good prediction, while the ones that match the entire lateral range up to the center of the river underpredict the PMZ significantly. These findings are of great importance for practitioners to characterize the geometry of the PMZ in rivers and for water quality modeling.