Importance of Vertical Variations of Velocity for Shear Dispersion in Rivers
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 10
Abstract
An expression for the dispersion coefficient in a rectangular channel is derived to evaluate the importance of transverse and vertical variations in velocity for dispersion. The contribution of vertical variations to dispersion depends not on the ratio of the width and depth of the channel—as is usually assumed—but on the ratio of mixing times, , where and are the transverse and vertical mixing coefficients, respectively. The analysis allows the role of vertical variations to be assessed quantitatively as a function of the time scale ratio and the shape of the velocity profile. The time scale ratio is estimated using data sets compiled by others and several empirical formulas for . In almost all cases, vertical variations contribute a small amount to the overall dispersion. The results support the usual practice of considering only transverse variations in computing the dispersion coefficient, and the analysis provides an approach for including vertical variations in calculations of dispersion in cases in which is not small.
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References
Bansal, M. K. (1971). “Dispersion in natural streams.” J. Hydraul. Div., 97(11), 1867–1886.
Barenblatt, G. I., and Chorin, A. J. (1996). “Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.” Proc. Nat. Acad. Sci., 93(13), 6749–6752.
Carr, M. L., and Rehmann, C. R. (2007). “Measuring the dispersion coefficent with acoustic Doppler current profilers.” J. Hydraul. Eng., 977–982.
Deng, Z. Q., Singh, V. P., and Bengtsson, L. (2001). “Longitudinal dispersion coefficient in straight rivers.” J. Hydraul. Eng., 919–927.
Elder, J. W. (1959). “The dispersion of marked fluid in turbulent shear flow.” J. Fluid Mech., 5(4), 544–560.
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 Press, New York.
Godfrey, R. G., and Frederick, B. J. (1970). “Stream dispersion at selected sites.” Professional Paper No. 433-K, U.S. Geological Survey, Washington, DC.
Jackson, P. R., Johnson, K. K., and Duncker, J. J. (2012). “Comparison of index velocity measurements made with a horizontal acoustic Doppler current profiler and a three-path acoustic velocity meter for computation of discharge in the Chicago sanitary and ship canal near Lemont, Illinois.”, U.S. Geological Survey, Reston, VA.
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.
Kashefipour, S. M., and Falconer, R. A. (2002). “Longitudinal dispersion coefficients in natural channels.” Water Res., 36(6), 1596–1608.
Kim, D. (2012). “Assessment of longitudinal dispersion coefficients using acoustic Doppler current profilers in large river.” J. Hydro-Environ. Res., 6(1), 29–39.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, U.K.
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.
Shen, C., Niu, J., Anderson, E. J., and Phanikumar, M. S. (2010). “Estimating longitudinal dispersion in rivers using acoustic Doppler current profilers.” Adv. Water Resour., 33(6), 615–623.
Taylor, G. I. (1953). “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proc. R. Soc. London A, 219, 186–203.
Young, W. R., and Jones, S. (1991). “Shear dispersion.” Phys. Fluids A, 3(5), 1087–1101.
Zauderer, E. (1989). Partial differential equations of applied mathematics, Wiley, New York.
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© 2015 American Society of Civil Engineers.
History
Received: Aug 19, 2014
Accepted: Mar 10, 2015
Published online: May 26, 2015
Published in print: Oct 1, 2015
Discussion open until: Oct 26, 2015
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