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A two-equation model for contaminant dispersion in natural streams

Published online by Cambridge University Press:  21 April 2006

Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK

Abstract

A simple two-equation model is derived which has the properties that the total contaminant exposure, the mean time of arrival, the temporal spread, and the skewness, are asymptotically correct at large distances downstream of a discharge. The role of changes in the breadth of a river upon the dispersion process is investigated by a means of an illustrative example. This reveals cubic dependence upon the breadth, and hence the great importance of wide reaches of rivers as regards contaminant dispersion.

Type
Research Article
Copyright
© 1987 Cambridge University Press

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References

Beer, T. & Young, P. C. 1983 Longitudinal dispersion in natural streams. J. Env. Engng 109, 10491067.Google Scholar
Chatwin, P. C. 1970 The approach to normality of the concentration distribution of a solute in solvent flowing along a straight pipe. J. Fluid Mech. 43, 321352.Google Scholar
Chatwin, P. C. 1980 Presentation of longitudinal dispersion data. J. Hydraul. Div. ASCE 106, 7183.Google Scholar
Fischer, H. B. 1969 The effects of bends on dispersion in streams. Wat. Resources Res. 5, 496506.Google Scholar
Nordin, C. F. & Sabol, G. V. 1974 Empirical data on longitudinal dispersion in rivers. U.S. Geological Survey. Rep. no. 20–74. 372 pp.Google Scholar
Smith, R. 1981 A delay-diffusion description for contaminant dispersion. J. Fluid Mech. 105, 469486.Google Scholar
Smith, R. 1983 Longitudinal dispersion coefficients for varying channels. J. Fluid Mech. 130, 299314.Google Scholar
Smith, R. 1984 Temporal moments at large distances downstream of contaminant releases in rivers. J. Fluid Mech. 140, 153174.Google Scholar
Sumer, S. M. 1976 Transverse dispersion in partially stratified tidal flow. Univ. California Berkley, Hydraul. Engng, Lab. Rep. WHM-20.Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186203.Google Scholar
Yotsukura, N. & Sayre, W. W. 1976 Transverse mixing in natural channels. Wat. Resources Res. 12, 695704.Google Scholar