Abstract
There are different approaches to estimating the transverse dispersion coefficient in river mixing. Theoretical approaches have derived the dispersion coefficient from the concept of shear flow, which has dominant effects on the transverse mixing. Empirical approaches have developed an equation using the hydraulic and geometric data of rivers through dimensional analysis and regression techniques. These two equations interact closely with each other. For example, the complicated theoretical equation can be simplified by empirical approaches, and the functional relationships of the empirical equation can be derived from theoretical bases. In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. As a regression method, the least-square iterative method was used because the equation was a nonlinear model. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the flow condition and the river geometry. Moreover, the proposed equation does not vary widely according to variation of flow conditions. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.
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References
Almquist CW, Holley ER (1985) Transverse mixing in meandering laboratory channels with rectangular and naturally varying cross sections. Technical Report CRWR-205, University of Texas
Baek KO, Seo IW (2011) Transverse dispersion caused by secondary flow in curved channels. J Hydraul Eng 137(10):1126–1134
Baek KO, Seo IW, Jung SJ (2006) Evaluation of dispersion coefficients in meandering channels from transient tracer tests. J Hydraul Eng 132(10):1021–1032
Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, New York
Beltaos S (1980) Transverse mixing tests in natural streams. J Hydraul Div ASCE 106(HY10):1607–1625
Boxall JB, Guymer I (2003) Analysis and prediction of transverse mixing coefficients in natural channels. J Hydraul Eng 129(2):129–139
Deng ZQ, Bengtsson L, Singh VP, Adrian DD (2002) Longitudinal dispersion coefficient in single-channel streams. J Hydraul Eng 128(10):901–916
Elder JW (1959) The dispersion of marked fluid in turbulent shear flow. J Fluid Mech 5:544–560
Fischer HB (1967) Transverse mixing in a sand-bed channel. Professional Paper No 575-D, US Geological Survey
Fischer HB (1969) The effect of bends on dispersion in streams. Water Resour Res 5(2):496–506
Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic Press, New York
Holley ER, Abraham G (1973) Field tests on transverse mixing in rivers. J Hydraul Div ASCE 99(HY12):2313–2331
Holly FM Jr, Nerat G (1983) Field calibration of stream-tube dispersion model. J Hydraul Eng 109(11):1455–1470
Jackman AP, Yotsukura N (1977) Thermal loading of natural streams. Professional paper No 991, US Geological Survey
Jeon TM, Baek KO, Seo IW (2007) Development of an empirical equation for the transverse dispersion coefficient in natural streams. Environ Fluid Mech 7(4):317–329
Krishnappan BG, Lau YL (1977) Transverse mixing in meandering channels with varying bottom topography. J Hydraul Res 15(4):351–371
Lau YL, Krishnappan BG (1981) Modeling transverse mixing in natural streams. J Hydraul Div ASCE 107(HY2): 209–226
Odgaard AJ (1986) Meander-flow model I: development. J Hydraul Eng 112(12):1117–1136
Rozovskii IL (1957) Flow of water in bends of open channels. Academy of Science of Ukrainian SSR, Kiew
Rutherford JC (1994) River mixing. Wiley, Chichester
Sayre WW (1979) Shore-attached thermal plumes in rivers. In: Shen HW (ed) Modelling in rivers. Wiley, London, pp 15.1–15.44
Seo IW, Baek KO (2004) Estimation of longitudinal dispersion coefficient using the velocity profile in natural streams. J Hydraul Eng 130(3):227–236
Seo IW, Baek KO, Jeon TM (2006) Analysis of transverse mixing in natural streams under slug tests. J Hydraul Res 44(3):350–362
Somlyody L (1982) An approach to the study of transverse mixing in streams. J Hydraul Res 20:203–220
Yotsukura N, Sayre WW (1976) Transverse mixing in natural channels. Water Resour Res 12(4):695–704
Yotsukura N, Fischer HB, Sayre WW (1970) Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa and Plattsmouth, Nebraska. Water Supply Paper No 1899-G, US Geological Survey
Acknowledgments
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012-0008575), and partly supported by a grant (11-TI-C06) from Construction Technology Innovation Program funded by Ministry of Land, Transport and Maritime Affairs of Korean government.
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Baek, K.O., Seo, I.W. Empirical equation for transverse dispersion coefficient based on theoretical background in river bends. Environ Fluid Mech 13, 465–477 (2013). https://doi.org/10.1007/s10652-013-9276-5
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DOI: https://doi.org/10.1007/s10652-013-9276-5