Transverse Dispersion Caused by Secondary Flow in Curved Channels
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 10
Abstract
A new theoretical equation is proposed to describe the streamwise variations of the transverse velocity along a curved channel with a constant curvature. Furthermore, based on this theoretical equation for the transverse velocity, a new equation for the transverse dispersion coefficient is developed to incorporate the effect of the secondary flow on the transverse dispersion in curved channels. The new equations for the transverse velocity and dispersion coefficient are verified with experimental data sets that were obtained from laboratory experiments conducted in two different channels. The results show that the proposed velocity equation properly describes the streamwise variations of the secondary flow developed in the curved channels. The reach-averaged values of the transverse dispersion coefficient calculated by the new equation are in relatively good agreement with the observed values from the laboratory channels. Sensitivity analysis reveals that both the secondary flow and the transverse dispersion coefficient are proportional to the roughness factor, and in inverse proportion to the aspect ratio of the channel.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research work was partly supported by the 21C Frontier project of the Ministry of Science and Technology of Korea, and the Construction Technology Innovation Program (08-Tech-Inovation-F01) through the Research Center of Flood Defense Technology for Next Generation of Ministry of Land, Transport and Maritime Affairs. This research was conducted in the Engineering Research Institute of Seoul National University, Seoul, Korea.
References
Albers, C., and Steffler, P. (2007). “Estimation transverse mixing in open channels due to secondary current-induced shear dispersion.” J. Hydraul. Eng., 133(2), 186–196.
Almquist, C. W., and Holley, E. R. (1985). “Transverse mixing in meandering laboratory channels with rectangular and naturally varying cross sections.” Technical Rep. CRWR-205, Univ. of Texas, Austin, TX.
Baek, K. O., and Seo, I. W. (2008). “ Prediction of transverse dispersion coefficient using vertical profile of secondary flow in meandering channels.” KSCE J Civ. Eng., 12(6), 417–426.
Baek, K. O., Seo, I. W., and Jung, S. J. (2006). “Evaluation of dispersion coefficients in meandering channels from transient tracer tests.” J. Hydraul. Eng., 132(10), 1021–1032.
Blanckaert, K., and Graf, W. H. (2004). “Momentum transport in sharp open-channel bends.” J. Hydraul. Eng., 130(3), 186–198.
Boxall, J. B., and Guymer, I. (2003). “Analysis and prediction of transverse mixing coefficients in natural channels.” J. Hydraul. Eng., 129(2), 129–139.
Chang, H. H. (1988). Fluvial processes in river engineering, Wiley, New York.
Chikwendu, S. C. (1986). “Calculation of longitudinal shear dispersivity using an N-zone model as .” J. Fluid Mech., 167, 19–30.
Deng, Z., Singh, V. P., and Bengtsson, L. (2001). “Longitudinal dispersion coefficient in straight rivers.” J. Hydraul. Eng., 127(11), 919–927.
Engelund, F. (1974). “Flow and bed topography in channel bends.” J. Hydraul. Div., 100(11), 1631–1648.
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 Press, New York.
Henderson, F. M. (1966). Open channel flow, Macmillan Publishing, New York.
Holley, E. R., Siemons, J., and Abraham, G. (1972). “Some aspects of analyzing transverse diffusion in rivers.” J. Hydraul. Res., 10(1), 27–57.
Johannesson, H., and Parker, G. (1989). “Secondary flow in mildly sinuous channel.” J. Hydraul. Eng., 115(3), 289–308.
Kikkawa, H., Kitagawa, A., and Ikeda, S. (1976). “Flow and bed topography in curved open channels.” J. Hydraul. Div., 102(9), 1327–1342.
Odgaard, A. J. (1986). “Meander-flow model I: Development.” J. Hydraul. Eng., 112(12), 1117–1136.
Rozovskii, I. L. (1957). Flow of water in bends of open channels, Academy of Science, Russia.
Schlichting, H. (1968). Boundary-layer theory, McGraw-Hill, New York.
Seo, I. W., Lee, M. E., and Baek, K. O. (2008). “2D modeling of heterogeneous dispersion in meandering channels.” J. Hydraul. Eng., 134(2), 196–204.
Taylor, G. (1954). “The dispersion of matter in turbulent flow through a pipe.” Proc. R. Soc. A, 223, 446–468.
Vriend, H. J. (1977). “A mathematical model of steady flow in curved shallow channels.” J. Hydraul. Res., 15(1), 37–54.
Yotsukura, N., and Sayre, W. W. (1976). “Transverse mixing in natural channels.” Water Resour. Res., 12(4), 695–704.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 10 • October 2011
Pages: 1126 - 1134
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Aug 7, 2009
Accepted: Mar 22, 2011
Published online: Mar 23, 2011
Published in print: Oct 1, 2011
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.