Explicit Estimates of Arrival Times for Dispersion in Rivers
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 11
Abstract
Explicit formulas for the times of arrival of the leading and trailing edges of a contaminant cloud are developed from a one-dimensional advection-dispersion model of transport. These times—defined as the times at which the concentration is some fraction of the peak concentration—can be determined easily with iterations using a spreadsheet or other software, but this approach becomes time-consuming if many calculations are needed. Also, solutions to the transient storage zone model and its relatives can be made more efficient by identifying the arrival times of the edges of a contaminant cloud. The expressions for the arrival times depend only the fraction and the Péclet number . For , the formula for the time of arrival of the leading edge is within 7% for and 1% for , and the expression for the time of arrival of the trailing edge is within 10–20% for and less than 1% for . Despite the criticisms of the advection-dispersion model for transport in real waterways, the formulas based on it predict the arrival times at least as well as previously proposed formulas, as long as the mean velocity over the river reach can be estimated.
Get full access to this article
View all available purchase options and get full access to this article.
References
De Smedt, F., Brevis, W., and Debels, P. (2005). “Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage.” J. Hydrol., 315(1–4), 25–39.
Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.” J. Hydr. Div., 93(HY6), 187–216.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic Press, New York.
Iwasa, Y., and Aya, S. (1991). “Predicting longitudinal dispersion coefficient in open-channel flows.” Environmental hydraulics, Vols. 1 and 2, J. H. W. Lee and Y. K. Cheung, eds., A.A. Balkema, Rotterdam, Netherlands, 505–510.
Jeon, T. M., Baek, K. O., and Seo, I. W. (2007). “Development of an empirical equation for the transverse dispersion coefficient in natural streams.” Environ. Fluid Mech., 7(4), 317–329.
Jobson, H. E. (1996). “Prediction of travel time and longitudinal dispersion in rivers and streams.”, U.S. Geological Survey, Washington, DC.
Jobson, H. E. (1997). “Predicting travel time and dispersion in rivers and streams.” J. Hydraul. Eng., 971–978.
Jobson, H. E. (2001). “Predicting river travel time from hydraulic characteristics.” J. Hydraul. Eng., 911–918.
Kashefipour, S. M., and Falconer, R. A. (2002). “Longitudinal dispersion coefficients in natural channels.” Water Res., 36(6), 1596–1608.
Kilpatrick, F. A., and Wilson, J. F. (1989). “Measurement of time of travel in streams by dye tracing.”, U.S. Geological Survey, Washington, DC.
Koussis, A. D., and Rodríguez-Mirasol, J. (1998). “Hydraulic estimation of dispersion coefficient for streams.” J. Hydraul. Eng., 317–320.
Liu, H. (1977). “Predicting dispersion coefficient of streams.” J. Environ. Eng. Div., 103(1), 59–69.
Nordin, C. F., and Sabol, G. V. (1974). “Empirical data on longitudinal dispersion in rivers.”, U.S. Geological Survey, Washington, DC.
Nordin, C. F., and Troutman, B. M. (1980). “Longitudinal dispersion in rivers: The persistence of skewness in observed data.” Water Resour. Res., 16(1), 123–128.
Rehmann, C. R., and Soupir, M. L. (2009). “Importance of interactions between the water column and the sediment for microbial concentrations in streams.” Water Res., 43(18), 4579–4589.
Rivord, J., Saito, L., Miller, G., and Stoddard, S. S. (2014). “Modeling contaminant spills in the Truckee River in the western United States.” J. Water Resour. Planning Manage., 343–354.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Schmalle, G. F., and Rehmann, C. R. (2014). “Analytical solution of a model of contaminant transport in the advective zone of a river.” J. Hydraul. Eng., 04014029.
Seo, I. W., and Baek, K. O. (2004). “Estimation of the longitudinal dispersion coefficient using the velocity profile in natural streams.” J. Hydraul. Eng., 227–236.
Seo, I. W., and Cheong, T. S. (1998). “Predicting longitudinal dispersion coefficient in natural streams.” J. Hydraul. Eng., 25–32.
Shucksmith, J., Boxall, J., and Guymer, I. (2007). “Importance of advective zone in longitudinal mixing experiments.” Acta Geophys., 55(1), 95–103.
Waldon, M. G. (1998). “Time-of-travel in the lower Mississippi River: Model development, calibration, and application.” Water Environ. Res., 70(6), 1132–1141.
Young, W. R., and Jones, S. (1991). “Shear dispersion.” Phys. Fluids A, 3(5), 1087–1101.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Nov 26, 2014
Accepted: Apr 9, 2015
Published online: Jun 12, 2015
Published in print: Nov 1, 2015
Discussion open until: Nov 12, 2015
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.