Longitudinal Dispersion Coefficient in Single-Channel Streams
Publication: Journal of Hydraulic Engineering
Volume 128, Issue 10
Abstract
Using a new channel shape equation for straight channels and a more versatile channel shape or local flow depth equation for natural streams a method is developed for prediction of the longitudinal dispersion coefficient in single-channel natural streams, including straight and meandering ones. The method involves derivation of a new triple integral expression for the longitudinal dispersion coefficient and development of an analytical method for prediction of this coefficient in natural streams. The proposed method is verified using 70 sets of field data collected from 30 streams in the United States ranging from straight manmade canals to sinuous natural rivers. The new method predicts the longitudinal dispersion coefficient, where more than 90% calculated values range from 0.5 to 2 times the observed values. The advantage of the new method is that it is capable of accurately predicting the longitudinal dispersion coefficient in single-channel natural streams without using detailed dye concentration test data. A comparison between the new method and the existing methods shows that the new method significantly improves the prediction of the longitudinal dispersion coefficient.
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References
Bencala, K. E., and Walters, R. A.(1983). “Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model.” Water Resour. Res., 19(3), 718–724.
Chang, H. H. (1988). Fluvial processes in river engineering, Wiley, New York, 10–27, 306–309.
Chatwin, P. C.(1971). “On the interpretation of some longitudinal dispersion experiments.” J. Fluid Mech., 48(4), 689–702.
Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, New York, 26–27, 98–125.
Czernuszenko, W. (1990). “Dispersion of pollutants in flowing surface waters.” Encyclopedia of fluid mechanics, Gulf, Houston, 119–169.
Czernuszenko, W., and Rowinski, P. M.(1997). “Properties of the dead-zone model of longitudinal dispersion in rivers.” J. Hydraul. Res., 35(4), 491–504.
Czernuszenko, W., Rowinski, P. M., and Sukhodolov, A.(1998). “Experimental and numerical validation of the dead-zone model for longitudinal dispersion in rivers.” J. Hydraul. Res., 36(2), 269–280.
Deng, Z.-Q., and Singh, V. P.(1999). “Mechanism and conditions for change in channel pattern.” J. Hydraul. Res., 37(4), 465–478.
Deng, Z.-Q., Singh, V. P., and Bengtsson, L.(2001). “Longitudinal dispersion coefficient in straight rivers.” J. Hydraul. Eng., 127(11), 919–927.
Elder, J. W.(1959). “The dispersion of a marked fluid in turbulent shear flow.” J. Fluid Mech., 5(4), 544–560.
Fernald, A. G., Wigington, Jr., P. J., and Landers, D. H.(2001). “Transient storage and hyporheic flow along the Willamette River, Oregon: field measurements and model estimates.” Water Resour. Res., 37(6), 1681–1694.
Fischer, B. H.(1967). “The mechanics of dispersion in natural streams.” J. Hydraul. Div., Am. Soc. Civ. Eng., 93(6), 187–216.
Fischer, H. B.(1969). “The effect of bends on dispersion in streams.” Water Resour. Res., 5(2), 496–506.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic. New York, 104–138.
Godfrey, R. G., and Fredrick, B. J. (1970). “Stream dispersion at selected sites.” Professional Rep. No. 433-K, U.S. Geological Survey.
Holley, E. R.(1969). “Unified view of diffusion and dispersion.” J. Hydraul. Div., Am. Soc. Civ. Eng., 95(2), 621–631.
Lau, Y. L., and Krishnappan, B. G.(1981). “Modeling transverse mixing in natural streams.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(2), 209–226.
Lees, J. M., Camacho, L. A., and Chapra, S.(2000). “On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams.” Water Resour. Res., 36(1), 213–224.
Liu, H.(1977). “Predicting dispersion coefficient of streams.” J. Environ. Eng. Div., Am. Soc. Civ. Eng., 103(1), 59–69.
Martin, J. L., and McCutcheon, S. C. (1999). Hydrodynamics and transport for water quality modeling, CRC, Boca Raton, Fla., 7–220.
McCutcheon, S. C. (1989). Water quality modeling, Vol. I, CRC, Boca Raton, Fla., 27–171.
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.
McQuivey, R. S., and Keefer, T. N.(1976). “Dispersion–Mississippi River below Baton Rouge, La.” J. Hydraul. Div., Am. Soc. Civ. Eng., 102(10), 1425–1437.
Nordin, C. F., and Sabol, G. V. (1974). “Empirical data on longitudinal dispersion in rivers.” Water Resources Investigations Rep. No. 20–74, U.S. Geological Survey.
Piasecki, M., and Katopodes, N. D.(1999). “Identification of stream dispersion coefficients by adjoint sensitivity method.” J. Hydraul. Eng., 125(7), 714–724.
Przedwojski, B., Blazejewski, R., and Pilarczyk, K. W. (1995). River training techniques: fundamentals, design and applications. A. A. Balkema, Rotterdam, The Netherlands, 302–319.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K., 102–200.
Schumm, S. A.(1963). “Sinuosity of alluvial rivers on the Great Plains.” Geol. Soc. Am. Bull., 74, 1089–1100.
Seo, I. W., and Cheong, T. S.(1998). “Predicting longitudinal dispersion coefficient in natural streams.” J. Hydraul. Eng., 124(1), 25–32.
Seo, I. W., and Cheong, T. S.(2001). “Moment-based calculation of parameters for the storage zone model for river dispersion.” J. Hydraul. Eng., 127(6), 453–465.
Sooky, A. A.(1969). “Longitudinal dispersion in open channels.” J. Hydraul. Div., Am. Soc. Civ. Eng., 95(4), 1327–1346.
Taylor, G. I.(1953). “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proc. R. Soc. London, Ser. A, 219, 186–203.
Taylor, G. I.(1954). “The dispersion of matter in turbulent flow through a pipe.” Proc. R. Soc. London, Ser. A, 223, 446–468.
Wörman, A.(2000). “Comparison of models for transient storage of solutes in small streams.” Water Resour. Res., 36(2), 455–468.
Yotsukura, N., Fischer, H. B., and Sayre, W. W. (1970). “Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa, and Plattsmouth, Nebraska.” Water-Supply Rep. No. 1899-G, U.S. Geological Survey.
Zhang, R. J., and Xie, J. H. (1993). Sedimentation research in China, China Water and Power Press, Beijing, 228–229.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 128 • Issue 10 • October 2002
Pages: 901 - 916
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Aug 23, 2001
Accepted: Apr 19, 2002
Published online: Sep 13, 2002
Published in print: Oct 2002
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