Mixing in Overland Flow during Rainfall
Publication: Journal of Environmental Engineering
Volume 116, Issue 4
Abstract
A method is presented for estimating vertical mixing coefficients in overland flow with rainfall using laboratory data and using a mathematical model of shear‐flow convection, rainfall dilution, and vertical mixing. The laboratory data consist of concentration‐time measurements downstream from an injection of a conservative dye into overland flow during rainfall over a smooth impervious surface with constant slope, without sediment and with flow in the laminar Reynolds number range. Results of the mathematical model are compared to the concentration time measurements to calibrate values of the vertical mixing coefficient. The calibrated values of the vertical mixing coefficient were most highly correlated to slope and a Reynolds number related to rainfall intensity. An analysis of the calibrated vertical mixing coefficient values using equations for eddy turbulence did not prove satisfactory.
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References
1.
Cleary, R. W., and Adrian, D. D. (1973). “New analytical solutions for dye diffusion equations.” J. Envir. Engrg. Div., ASCE, 99(3), 213–227.
2.
Elder, J. W. (1959). “The dispersion of marked fluid in turbulent shear flow.” J. Fluid Mech., 5(4), 544–560.
3.
Engle, O. G. (1966). “Crater depth in fluid impacts.” J. Appl. Phys., 37(4), 1798–1808.
4.
Engle, O. G., (1967). “Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts.” J. Appl. Phys. 38 (10), 3935–3940.
5.
Ferreira, A. G., Larock, B. E., and Singer, M. J. (1985). “Computer simulation of water drop impact in a 9.6‐mm deep pool.” Soil Sci. Soc. Am. J., 49(6), 1502–1507.
6.
Fischer, H. B. (1966). “A note on the one‐dimensional dispersion model.” Air and Water Pollution Int. J., 10, 443–452.
7.
Fischer, H. B. (1968). “Methods for predicting dispersion coefficients in natural streams with applications to lower reaches of the Green and Duwamish Rivers, Washington.” Professional Paper 582‐A, U.S. Geological Survey, Washington, D.C.
8.
Fischer, H. B. (1977). Discussion of “Convective Model of Longitudinal Dispersion.” J. Hydr. Div., ASCE, 103(8), 948–949.
9.
Fischer, H. B., et al. (1979). Mixing in inland and coastal waters. Academic Press, New York, N.Y.
10.
Harden, T. O., and Shen, H. T. (1972). “Numerical simulation of mixing in natural rivers.” J. Hydr. Div., ASCE, 105(4), 393–408.
11.
Harlow, F. H., and Shannon, J. P., (1967a). “Distortion of a splashing liquid drop.” Science, 157 (3788), 547–550.
12.
Harlow, F. H., and Shannon, J. P. (1967b). “The splash of a liquid drop.” J. Appl. Phys., 38(10), 3855–3866.
13.
Holley, E. R. (1969). “Unified view of diffusion and dispersion.” J. Hydr. Div., ASCE, 95(2), 621–631.
14.
Holley, E. R., Jr., and Harleman, D. R. F. (1965). “Dispersion of pollutants in estuary type flows.” Report No. 74, Hydrodynamics Lab., Massachusetts Inst. Of Tech., Cambridge, Mass.
15.
Macklin, W. C., and Metaxas, G. J. (1976). “Splashing of drops on liquid layers.” J. Appl. Phys., 47(9), 3963–3970.
16.
Mutchler, C. K. (1967). “Parameters for describing raindrop splash.” J. Soil and Water Conservation, 22(3), 91–94.
17.
Mutchler, C. K., and Hansen, L. M., (1970). “Splash of a waterdrop at terminal velocity.” Science, 169 (3952), 1311–1312.
18.
Palmer, R. S. (1965). “Waterdrop impact forces.” Trans. American Society of Agricultural Engineers, 8(1), 69–70,72.
19.
Shen, H. W., and Li, R. M. (1973). “Rainfall effect on sheet flow over smooth surface.” J. Hydr. Div., ASCE, 99(5), 771–792.
20.
Spalding, D. B. (1963). Convective mass transfer. McGraw‐Hill Book Co., New York, N.Y.
21.
Taylor, G. E. (1954). “The dispersion of matter in turbulent flow through a pipe.” Proc., Royal Society of London, Series A, 223, 445–468.
22.
Wang, R. C., and Wenzel, H. G. (1970). “The mechanics of a drop after striking a stagnant water layer.” Res. Report No. 30, Water Resour. Ctr., Univ. of Illinois, Urbana, Ill.
23.
Yeh, G.‐T., and Tsai, Y.‐J. (1976). “Dispersion of water pollutants in a turbulent shear flow.” Water Resour. Res., 12(6), 1265–1270.
24.
Yoon, Y. N. (1970). “The effect of rainfall on the mechanics of steady spatially varied sheet flow on a hydraulically smooth boundary,” thesis presented to the University of Illinois, at Urbana‐Champaign, Ill., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
25.
Yoon, Y. N., and Wenzel, H. G. (1971). “Mechanics of sheet flow under simulated rainfall.” J. Hydr. Div., ASCE, 97(9), 1367–1386.
26.
Yotsukura, N., and Cobb, E. D. (1972). “Transverse diffusion of solutes in natural streams.” Professional Paper 582‐C, U.S. Geological Survey, Washington, D.C.
27.
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 Environmental Engineering
Volume 116 • Issue 4 • July 1990
Pages: 764 - 784
Copyright
Copyright © 1990 ASCE.
History
Published online: Jul 1, 1990
Published in print: Jul 1990
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