Dispersion Coefficient of Streams from Tracer Experiment Data
Publication: Journal of Environmental Engineering
Volume 129, Issue 6
Abstract
The paper deals with a method for optimal identification of the dispersion coefficient for streams from observed concentration profiles at downstream sections (at least two sections are required) following injection of an environmentally safe tracer at an upstream section. The method makes use of the exact solution of the one-dimensional advection-dispersion equation. A reliable and accurate procedure is proposed for routing an arbitrary concentration variation further downstream using the convolution equation and pulse kernels. The new method does not require the frozen cloud approximation and avoids the error due to numerical integration of the convolution integral used for routing the concentration. It employs the objective criterion of minimum integral squared errors between observed and computed concentrations. Application of the method to field data sets shows that reliably accurate estimates of the dispersion coefficient are obtained.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bansal, M. K.(1971). “Dispersion in natural streams.” J. Hydraul. Div., Am. Soc. Civ. Eng., 97(11), 1867–1886.
Bear, J. (1972). Dynamics of fluid flow in porous media, Elsevier, New York.
Bear, J., and Todd, D. K. (1960). “The transition zone between fresh and salt waters in coastal aquifers.” Water Resour. Center Contrib. No. 29, Univ. of California.
Beck, M. B., and Young, P. C.(1975). “A dynamic model for DO-BOD relationships in a non-tidal stream.” Water Res., 9, 769–776.
Beer, T., and Young, P. C.(1983). “Longitudinal dispersion in natural streams.” J. Environ. Eng., 109(5), 1049–1067.
Chatwin, P. C.(1971). “On the interpretation of some longitudinal dispersion experiments.” J. Fluid Mech., 48, 689–702.
Day, T. J.(1975). “Longitudinal dispersion in natural channels.” Water Resour. Res., 11, 909–918.
Day, T. J., and Wood.(1976). “Similarity of mean motion of fluid particles dispersing in a natural channel.” Water Resour. Res., 12(4), 655–666.
Einstein, A.(1905). “Uber die von der molecular-kinetischen Theorie der Warme geoforderte Bewegung von in Ruhenden Flussigeiten suspendierten Teinchen.” Ann. Phys. (Leipzig), 17, 539–560.
Elder, J. W.(1959). “The dispersion of a marked fluid in turbulent shear flow.” J. Fluid Mech., 5(4), 544–560.
Fischer, H. B.(1968). “Dispersion prediction in natural streams.” J. Sanit. Eng. Div., Am. Soc. Civ. Eng., 94(5), 927–941.
Fischer, H. B.(1975). “Discussion on ‘Simple method of predicting dispersion in streams’ by R. S. McQuivey and T. N. Keefer.” J. Environ. Eng., 101(3), 453–455.
Fischer, H. B., List, E. J., Kohr, C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, New York.
Liu, H.(1977). “Predicting dispersion coefficient of streams.” J. Environ. Eng., 103(1), 59–69.
Magazine, M. K., Pathak, S. K., and Pande, P. K.(1988). “Effect of bed and side roughness on dispersion in open channels.” J. Hydraul. Eng., 114(7), 766–782.
Manklow, S. J. (1988). “Experimental and mathematical analysis of stream dispersion.” M.Sc. thesis, Imperial College of Science and Technology, London.
Marquardt, D. W.(1963). “An algorithm for least square estimation of nonlinear parameters.” J. Soc. Ind. Appl. Math., 11, 431–441.
McQuivey, R. S., and Keefer, T. N.(1974). “Simple method for predicting dispersion in streams.” J. Environ. Eng. Div., Am. Soc. Civ. Eng., 100(4), 997–1011.
Morel-Seytoux, H. J. (1975). “Optimal and legal conjunctive operation of surface and ground waters.” Proc., 2nd World Congress, Int. Water Resoure Association, New Delhi, India, Vol. IV, 119–129.
Nordin, C. F., Jr., and Troutman, B. M.(1980). “Longitudinal dispersion in rivers, the persistence of skewness in observed data.” Water Resour. Res., 16, 123–128.
Ogata, A. (1958). “Dispersion in porous media.” PhD thesis, Northwestern Univ., Evanston, Ill.
Ogata, A., and Banks, R. B. (1961). “A solution of differential equation of longitudinal dispersion in porous media.” USGS Prof. Pap. 441-A.
Parker, F. L.(1961). “Eddy diffusion in reservoirs and pipelines.” J. Hydraul. Div., Am. Soc. Civ. Eng., 95(4), 1327–1346.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Scheidegger, A. E.(1961). “General theory of dispersion in porous media.” J. Geophys. Res., 66, 3273–3278.
Stefan, H. G., and Demetracopoulos, A. C.(1981). “Cells in-series simulation of riverine transport.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(6), 675–697.
Taylor, G. I.(1921). “Diffusion by continuous movements.” Proc., London Math. Soc., 2(20), 196–212.
Taylor, G. I.(1953). “Dispersion of soluble matter in solvent flowing through a tube.” Proc. R. Soc. London, Ser. A, A219, 186–203.
Taylor, G. I.(1954). “The dispersion of matter in turbulent flow through pipe.” Proc. R. Soc. London, Ser. A, A223, 446–468.
Thackston, E. L., Hays, J. R., and Krenkel, P. A.(1967). “Least square estimation of mixing coefficients.” J. Sanit. Eng. Div., Am. Soc. Civ. Eng., 93(2), 47–58.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 129 • Issue 6 • June 2003
Pages: 539 - 546
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Sep 25, 2000
Accepted: Apr 23, 2002
Published online: May 15, 2003
Published in print: Jun 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.