Longitudinal dispersion in laboratory and natural streams

Abstract

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream. Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required. Large values of the dimensionless dispersion coefficient D/rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio. A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments. Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington. Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factory of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.