Analytical Solution of a Model of Contaminant Transport in the Advective Zone of a River
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 7
Abstract
An analytical solution of a model of contaminant transport in the advective zone of rivers is presented and evaluated. An existing model that accounts for transport in the advective zone by dividing the channel into flowing and stagnant zones is solved with Laplace transforms for the case of a Gaussian pulse injected into the center of the channel. The effects of the two main parameters of the model, the fraction of the channel occupied by the stagnant zone and a transfer coefficient, are consistent with expectations from the theory of shear dispersion. Another parameter, which is related to the streamwise width of the initial pulse, determines whether a separate pulse appears in the tracer-response curves. A procedure for determining the parameters from temporal moments of measured concentration curves is described and applied to measurements in the advective zone of a mountain stream. Predictions from the model of Reichert and Wanner fit the measurements—especially the peak concentration—better than predictions from the one-dimensional model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank Elizabeth Held for her help with computing the moments and preparing Fig. 3(b).
References
Albers, C., and Steffler, P. (2007). “Estimating transverse mixing in open channels due to secondary current-induced shear dispersion.” J. Hydraul. Eng., 186–196.
Boxall, J. B., and Guymer, I. (2003). “Analysis and prediction of transverse mixing coefficients in natural channels.” J. Hydraul. Eng., 129–139.
Davis, P. M., Atkinson, T. C., and Wigley, T. M. L. (2000). “Longitudinal dispersion in natural channels: 2. The roles of shear flow dispersion and dead zones in the River Severn, U.K.” Hydrol. Earth Syst. Sci., 4(3), 355–371.
Day, T. J. (1975). “Longitudinal dispersion in natural channels.” Water Resour. Res., 11(6), 909–918.
Day, T. J., and Wood, I. R. (1976). “Similarity of mean motion of fluid particles dispersing in a natural channel.” Water Resour. Res., 12(4), 655–666.
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. Hydraul. Div., 93(6), 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, New York.
Gualtieri, C. (2010). “RANS-based simulation of transverse turbulent mixing in a 2D geometry.” Environ. Fluid Mech., 10(1–2), 137–156.
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.
Pagsuyoin, S. A., Lung, W. S., and Colosi, L. M. (2012). “Predicting EDC concentrations in a river mixing zone.” Chemosphere, 87(10), 1111–1118.
Reichert, P., and Wanner, O. (1991). “Enhanced one-dimensional modeling of transport in rivers.” J. Hydraul. Eng., 1165–1183.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
Schmalle, G. F., and Rehmann, C. R. (2012). “Estimating contaminant transport in the advective zone.” Proc., 2012 Hydraulic Measurements and Experimental Methods Conf., American Society of Civil Engineers.
Shucksmith, J., Boxall, J., and Guymer, I. (2007). “Importance of advective zone in longitudinal mixing experiments.” Acta Geophys. Pol., 55(1), 95–103.
Sneddon, I. H. (1972). The use of integral transforms, McGraw-Hill, New York.
Ye, J., and McCorquodale, J. A. (1998). “Simulation of curved open channel flows by 3D hydrodynamic model.” J. Hydraul. Eng., 687–698.
Yotsukura, N., and Sayre, W. W. (1976). “Transverse mixing in natural channels.” Water Resour. Res., 12(4), 695–704.
Zhang, W. (2011). “A 2-D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient.” Water Resour. Res., 47(7), W07533.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 20, 2013
Accepted: Feb 10, 2014
Published online: Mar 25, 2014
Published in print: Jul 1, 2014
Discussion open until: Aug 25, 2014
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.