Longitudinal Dispersion in Rivers

by Spyridon Beltaos, Research Scientist; Environmental Hydr. Section, Hydr. Div., National Water Research Inst., Canada Centre for Inland Waters, Burlington, Ontario, Canada; formerly, Research Officer, Alberta Research Council, Edmonton, Canada,

Serial Information: Journal of the Hydraulics Division, 1980, Vol. 106, Issue 1, Pg. 151-172

Document Type: Journal Paper


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.

Subject Headings: Rivers and streams | Parameters (statistics) | Hydrologic models | Field tests | Computer networks | Linear functions | Curvature | High-rise buildings

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