Solute transport in overland flow during rainfall
Date
1985
Authors
Peyton, R. Lee, Jr., author
Sanders, Thomas G., advisor
Adrian, Donald Dean, committee member
Smith, Roger E., committee member
Shen, Hsieh W., committee member
Ward, Robert C., committee member
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Abstract
A numerical model was developed to simulate the movement of a conservative solute in steady overland flow over a smooth impervious plane under a constant rainfall intensity. This movement was described by shear-flow convection, vertical mixing, and rainfall dilution. Mass was converted in flow layers whose velocities varied according to velocity profile relationships developed in this study. Vertical diffusion occurred between flow layers according to the Fickian equation. Mass was diluted due to increasing depth of flow downstream. This model closely reproduced results of several analytical solutions for solute transport in steady, uniform flow. The model was then calibrated to results from overland flow laboratory experiments using the vertical mixing coefficient, Ɛ ƴ, as a calibration parameter. A regression analysis was used to relate the calibrated Ɛ ƴ values to rainfall and flow variables. The resulting regression equation showed that Ɛ ƴ increased with increasing rainfall intensity and with decreasing mean flow velocity. Ɛ ƴ varied the greatest at low rainfall intensities and near the top of the overland flow plane. The lower range of the calibrated Ɛ ƴ values compared favorably with the molecular diffusion coefficient for the dye tracer used in the laboratory experiments, while the upper range was similar to theoretical vertical mixing coefficients for steady, uniform, turbulent flow at equivalent discharges. It was concluded that the velocity of the peak concentration can vary between the mean cross-sectional velocity and the maximum point velocity, depending on the Ɛ ƴ value. It was further concluded that rainfall generally does not produce a continuous state of complete vertical mixing in overland flow. The study was then taken one step further by using the resulting Ɛ ƴ equation to examine the length of the convective distance beyond which Taylor's one-dimensional dispersion analogy is generally valid. This distance was found to be very short where vertical mixing was great and very long where vertical mixing was small. In addition, the Ɛ ƴ equation was used along with Fischer's theoretical expression for the one-dimensional dispersion coefficient for open-channel flow (based on Taylor's research with pipe flow) to compute dispersion coefficients for overland flow during rainfall. In some cases, negative dispersion coefficients were computed. In further checking the applicability of Fischer's expression, it was concluded that it is not appropriate for all velocity profiles.
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Subject
Runoff -- Mathematical models
Rain and rainfall