William W. Sayre | USGS Science

USGS1970

Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa, and Plattsmouth, Nebraska

Measurements of longitudinal dispersion, transverse mixing, channel geometry, and transverse velocity distribution were made in the Missouri River at a flow of about 33,000 cubic feet per second. The results show that the longitudinal dispersion coefficient for the 141-mile reach from Sioux City, Iowa, to Plattsmouth, Nebr., is about 16,000 square feet per second (approximately 5,600 U*d, where U* is the shear velocity and d is mean depth). The transverse mixing coefficient, Ez, for a 6-mile reach immediately downstream from Blair, Nebr., is about 1.3 square feet per second (approximately 0.6 U*d). The value of the longitudinal dispersion coefficient is one of the largest ever measured, and the value of the ratio Ez/U*d is approximately three times as large as that frequently reported for small straight channels.

Water Supply Paper↗

USGS1964

Exploratory laboratory study of lateral turbulent diffusion at the surface of an alluvial channel

In natural streams turbulent diffusion is one of the principal mechanisms by which liquid and suspended-particulate contaminants are dispersed in the flow. A knowledge of turbulence characteristics is therefore essential in predicting the dispersal rates of contaminants in streams. In this study the theory of diffusion by continuous movements for homogeneous turbulence is applied to lateral diffusion at the surface of an open channel in which there is uniform flow. An exploratory-laboratory investigation was conducted in which the lateral dispersion at the water surface of a sand-Led flume was studied by measuring the lateral spread from a point source of small floating polyethylene articles. The experiment was restricted to a single set of low and channel geometry conditions. The results of the study indicate that with certain restrictions lateral dispersion in alluvial channels may be successfully described by the theory of diffusion by continuous movements. The experiment demonstrates a means for evaluating the lateral diffusion coefficient and also methods for quantitatively estimating fundamental turbulence properties, such as the intensity and the Lagrangian integral scale of turbulence in an alluvial channel. The experimental results show that with increasing distance from the source the coefficient of lateral turbulent diffusion increases initially but tends toward a constant limiting value. This result is in accordance with turbulent diffusion theory. Indications are that the distance downstream from the source required for the diffusion coefficient to reach its limiting value is actually very small when compared to the length scale of most diffusion phenomena in natural streams which are of practical interest.

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