Measuring the Dispersion Coefficient with Acoustic Doppler Current Profilers

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Abstract: A method is evaluated for estimating the longitudinal dispersion coefficient K from velocities and bathymetry measured with an acoustic Doppler current profiler ADCP. If shear dispersion controls the mixing, the dispersion coefficient can be estimated from measurements of velocity and depth in a cross section. The dispersion coefficient has typically been measured by costly and timeconsuming tracer studies because the velocity field could not be resolved sufficiently before the flow changed. However, ADCP transects, which now ar e routinely used to measure discharge, provide detailed velocity and bathymetry data quickly. The dispersion coefficient isestimated from ADCP measurements from the United States Geological Survey and compared with estimates from dye studies. Half of the estimates of K fall within 50% of the values from tracer studies, and 85% are within a factor of 3. The ADCP method is at least as accurate as the best empirical formula considered. Both the comparison of field data and an analysis with theoretical velocity profiles suggest that the error in K will be largest when the velocity profile is nearly uniform.

DOI: 10.1061/ASCE0733-94292007133:8977
CE Database subject headings: Acoustic techniques; Flow measurement; Dispersion; Rivers; Velocity; Tracers; Currents.

Introduction
Predicting the spread of contaminants is important for managing and protecting rivers and streams. To simulate contaminant dispersion, most mixing models require a longitudinal dispersion coefficient, which depends on the river geometry and flow. The dispersion coefficient has generally been estimated with empirical formulas or costly field tracer experiments. However, empirical formulas estimate K only within an order of magnitude Rutherford 1994. Tracer studies are considered more accurate, but the results apply for only the reach examined and the flow and weather during the study. Tracer studies also require a large investment in planning, staff, and analysis. Another approach to determining the longitudinal dispersion coefficient is to estimate it directly from the theory of shear dispersion with Fischer 1967

Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana–Champaign, 205 N. Mathews Ave., 2524 Hydrosystems
Laboratory, Urbana, IL 61801. E-mail: mcarr1@uiuc.edu 2 Assistant Professor, Dept. of Civil, Construction, and Environmental Engineering, Iowa State Univ., 374 Town Engineering Building, Ames, IA 50011. E-mail: rehmann@iastate.edu

Note. Discussion open until January 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this technical note was submitted for review and possible publication on July 18, 2005; approved on December 28, 2006. This technical note is part of the Journal of Hydraulic Engineering, Vol. 133, No. 8, August 1, 2007. ©ASCE, ISSN 0733-9429/2007/8- 977–982/$25.00. Dy transverse mixing coefficient; uy=uy−Uvelocity deviation; uydepth-averaged streamwise velocity; and U velocity averaged over the cross section. This equation assumes that shear dispersion, the mixing caused by particles experiencing different velocities as they are randomly diffused back and forth across the river by transverse dispersion, is the main mixing mechanism in the longitudinal direction.

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