Characteristics of transverse mixing in open-channel flows

Abstract

The transverse spreading of a plume generated by a point source in a uniform open-channel flow is investigated. A neutrally-buoyant tracer was injected continuously at ambient velocity through a small round source at a point within the flow. Tracer concentration was measured in situ at several points downstream of the source using conductivity probes. Tracer concentration was analyzed in two phases. In Phase I, time-averaged concentration was evaluated, its distribution within the plume determined, and characteristic coefficients of transverse mixing calculated. It was shown that the transverse mixing coefficient varied with the flow level and was highest near the water surface where flow velocity was greatest. In contrast to previous speculation, the ratio of the depth-averaged coefficient of transverse mixing D-_z to the product of the (bed) shear velocity u_* and the flow depth d was not a constant but depended on the aspect ratio γ = d/W, where W = flume width. For laboratory experiments D-_z/u_*d decreased from .024 to 0.093 as γ increased from 0.015 to 0.200. In Phase II, the temporal fluctuation of tracer concentration was studied in three sections. In the first, the intermittency factor technique was used to delineate three regions of the plume cross section: an inner core where tracer concentration c(t) was always greater than the background C_b; an intermittency region where c(t) was only intermittently greater than C_b; and the outer region where C_b was never exceeded. Dimensional analysis furnished universal curves for prediction of the geometric characteristics of the three regions. In the second section, the entire plume, at a fixed station, was treated as a fluctuating cloud. Variances characterizing the fluctuation of the plume centroid and the variation of the plume width were calculated and compared. In the third section, the intensity and probability density of the concentration fluctuations at fixed points were calculated. The distribution of the peak-to-average ratio was also determined. Finally the results of the two phases of study were interrelated to evaluate their contributions to the transverse spreading of the plume.