Longitudinal Dispersion in Rivers

Abstract

To explain the frequent deviation of longitudinal dispersion observations in rivers from the Fickian dispersion theory, a two-parameter model is developed. This model is based on reevaluation of the mixing length concept and the assumption that the characteristic irregularity of rivers retards the onset of the Fickian process. The model suggests that there are three distinct dispersion ranges. Within a characteristic stream length from the source, the temporal spread of the dispersing cloud increases linearly with distance; concentration-time curves at different locations along the stream are similar and can be predicted if a dimensionless coefficient is known. The Fickian process occurs at distances exceeding about three times the characteristic stream length. Transitional behavior occurs in the intermediate range. Published field data are analyzed to test the model and evaluate the dispersion parameters. The river length marking onset of Fickian dispersion is found to be up to 30 times that of a corresponding prismatic channel; it is estimated that Fickian dispersion is not likely to occur within lengths of practical interest in any but small streams.