Turbulent Mixing and Dispersion in Rivers

In the case of mixing primarily due to turbulent diffusion and dispersion, the Fickian transport coefficients are essentially independent of the chemical, so that the values of D determined from tracer experiments can be applied to other chemicals of interest in the same river. Two types of commonly used tracers are salts, such as sodium chloride (NaCl), and fluorescent dyes, such as rhodamine, which can be measured at very low concentrations. 

FIGURE 2-4 Transport of a chemical in a river. At time zero, a pulse injection is made at a location defined as distance zero in the river. As shown in the upper panel, at successive times C, t2, and t3, the chemical has moved farther downstream by advection, and also has spread out lengthwise in the river by mixing processes, which include turbulent diffusion and the dispersion associated with nonuniform velocity across the river cross section. Travel time between two points in the river is defined as the time required for the center of mass of chemical to move from one point to the other. Chemical concentration at any time and distance may be calculated according to Eq. [2-10]. As shown in the lower panel, Cmax, the peak concentration in the river at any time t, is the maximum value of Eq. [2-10] anywhere in the river at that time. The longitudinal dispersion coefficient may be calculated from the standard deviation of the concentration versus distance plot, Eq. [2-7]. 

Rivers are generally considered as a plug flow reactor with dispersion (Levenspiel, 1960), where the mixing is provided by the velocity profile and turbulence in the flow field. This concept is applied to the measurement of K /H = Kia in rivers, where H is depth of flow and K a = Ki AIV = K2 is generally called the reaeration coefficient, and a is the specific surface area. 

Figure 24.4 Mixing processes in a river. Ey and E, are the turbulent diffusion coefficients in the lateral and vertical direction, respectively h0 is the maximum depth. Longitudinal dispersion, djs, results from the variation of velocity in a given cross section of the river. A pollutant added to the river in cross section A-B mixes vertically and laterally into the whole river cross-section.

Vertical turbulent diffusion rates are usually sufficiently fast that vertical homogeneity can be assumed. A typical vertical dispersion coefficient is 100 cm /s or 0.01 m /s thus a characteristic time for vertical mixing in a 1 m deep river is about 100 s or a few minutes. If the water residence time in the reach is 2000 s (e.g., a 1000 m reach with a velocity of 0.5 m/s) vertical mixing is essentially complete and vertical homogeneity can be assumed. 

---