Transverse mixing in natural streams

Abstract

The mechanics of mixing of neutral substances in natural streams and methods for engineering applications of the understanding developed to date constitute the subject of this paper.Diffusion and differential advection are identified as the main processes governing mixing in natural streams and are reviewed in some detail. The interaction between these two processes is shown to enhance the rates of spreading in the longitudinal direction and this effect is termed dispersion.Methods for predicting the concentration resulting from injection of a neutral substance in a stream, as a function of time and location, are outlined and the various pertinent simplifications and associated assumptions are discussed. It is shown that in steady-state situations, such as those resulting from continuous releases at constant rate, analytical predictions are possible using a transformation that substitutes distance across the channel by the corresponding fraction of discharge. However, transient mixing, such as that resulting from slug or time-dependent injections, is a relatively complex process and requires use of numerical techniques of computation.A method for generating hydraulic information necessary for applications from limited data is presented. This can be used when detailed hydraulic data are not available or when only limited accuracy of prediction is required.Engineering application is shown to depend on knowledge of the transverse mixing coefficient. In straight, prismatic channels, this reflects the combined effects of turbulent diffusion and dispersion due to secondary currents. However, in natural streams, this coefficient incorporates additional effects, such as transverse dispersion due to helical motions at river bends and river nonuniformity. The former effect has been well documented but virtually nothing is known about the latter.Experimental data regarding the transverse mixing coefficient are reviewed for straight and meandering laboratory channels as well as natural streams. It is shown that the available field data are not sufficient to permit predictions of the transverse mixing coefficient in terms of stream hydraulics. Qualitatively, it can be stated that when the mixing coefficient represents an average value over several meanders, the curvature of river bends appears to be of less significance than had been thought previously and the effect of an ice cover seems to be better accounted for if the transverse mixing coefficient is nondimensionalized with the frictional velocity and the depth rather than the hydraulic radius.Finally, an example of practical application is presented.