Estimating Transverse Mixing in Open Channels due to Secondary Current-Induced Shear Dispersion
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 2
Abstract
For transverse mixing problems in open channels, the effect of secondary currents on a tracer cloud is to disperse and mix the tracer in three dimensions more rapidly than would be the case if transverse turbulent diffusion were acting alone. Transverse mixing of this kind is difficult to simulate using two-dimensional depth-averaged mixing models which typically requires the specification of an equivalent dispersivity combining the effects of vertical shear dispersion and horizontal turbulent diffusion. In this paper, a two-dimensional vertically averaged and moment (VAM) equation technique for describing the transverse mixing mechanics of passive tracer vertical shear dispersion in approximately uniform curved open channel flow is detailed. An analytical expression is generated and compared to previous works in the literature describing the longitudinal development and asymptotic value of transverse dispersivity due to secondary current vertical shear dispersion. This expression is shown to describe the changing value of dispersivity even within the advective zone where traditional two-dimensional models cannot be applied. Distributions of depth-averaged concentration generated from numerical simulations of the VAM equations are compared to other higher fidelity computational results. The practical value of this VAM analysis framework is discussed relative to the potential for implementation in modern river modeling software packages.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first writer would like to acknowledge financial support provided by the Canadian Federal Government Department of Fisheries and Oceans through Mr. Chris Katopodis whose support and guidance throughout the overall research project significantly facilitated the writing of this paper.
References
Aris, R. (1956). “On the dispersion of a solute in a fluid flowing through a tube.” Proc. R. Soc. London, Ser. A, 235A, 67–77.
Boxall, J., and Guymer, I. (2003). “Analysis and prediction of transverse mixing coefficients in natural channels.” J. Hydraul. Eng., 129(2), 129–139.
Boxall, J., Guymer, I., and Marion, A., (2003). “Transverse mixing in sinuous natural open channel flows.” J. Hydraul. Res., 41(2), 152–165.
Chang, Y. C. (1971). Lateral mixing in meandering channels, Ph.D. thesis, University of Iowa, Iowa City, Iowa.
Elder, J. W. (1959). “The dispersion of marked fluid in turbulent shear flow.” J. Fluid Mech., 5, 544–560.
Elhadi, N., Harrington, I., Lau, Y. L., and Krishnappan, B. G. (1984). “River mixing—A state-of-the-art report.” Can. J. Civ. Eng., 11, 580–609.
Fischer, H. B. (1969). “The effect of bends on dispersion in streams.” Water Resour. Res., 5, 909–915.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, San Diego.
Ghamry, H., and Steffler, P. (2002a). “Two dimensional vertically averaged and moment equations for rapidly varied flows.” J. Hydraul. Res., 40(5), 579–587.
Ghamry, H., and Steffler, P. (2002b). “Effect of applying different distribution shapes for velocities and pressure on simulation of curved open channels.” J. Hydraul. Eng., 128(11), 969–982.
Holly, F. M. (1985). “Dispersion in rivers and coastal waters. I: Physical principals and dispersion equations.” Developments in hydraulic engineering 3, P. Novak, ed., Elsevier Applied Science, London, 1–37.
Holley, E. R., Siemons, J., and Abraham, G. (1972). “Some aspects of analyzing transverse diffusion in rivers.” J. Hydraul. Res., 10, 27–57.
Kobayashi, M. H., and Pereira, J. C. H. (1996). “A comparison of second order convection discretization schemes for incompressible flow.” Commun. Numer. Methods Eng., 12, 395–411.
Lau, Y. L., and Krishnappan, B. G. (1981). “Modeling transverse mixing in natural streams.” J. Hydr. Div., 107(3), 209–226.
Rozovskii, I. L. (1957). Flow of water in bends of open channels, Academy of Sciences of the Ukrainian SSR, Kiev, translation No. OTS 60-51133, Office of Technical Services, U.S. Department of Commerce, Washington, D.C.
Rutherford, J. C. (1994). River mixing, Wiley, New York.
Sayre, W. W. (1973). “Natural mixing processes in rivers.” Environmental impact on rivers, H. W. Shen, ed., Fort Collins, Colo., Chap. 6.
Sayre, W. W., and Chang, F. M. (1968). “A laboratory investigation of open-channel dispersion processes for dissolved, suspended, and floating dispersants.” U.S. Geological Survey Professional Paper 433-E, Wash.
Steffler, P. M., and Jin, Y. C. (1993). “Depth-averaged and moment equations for moderately shallow free surface flow.” J. Hydraul. Res., 31(1), 5–17.
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, 233, 446–468.
Yotsukura, N. (1977). “Derivation of solute-transport equations for a turbulent natural channel flow.” J. Res., U.S. Geological Survey, 5, 277–284.
Yotsukura, N., and Cobb, E. D. (1972). “Transverse diffusion of solutes in natural streams.” U.S. Geological Survey Professional Paper 582-C, Wash.
Yotsukura, N., and Sayre, W. W. (1976). “Transverse mixing in natural channels.” Water Resour. Res., 12(4), 695–704.
Information & Authors
Information
Published In
Copyright
© 2007 American Society of Civil Engineers.
History
Received: Apr 27, 2005
Accepted: Jul 6, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
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.