Rivers Fickian transport

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 3-17 Dispersion of a pulse of a tracer substance in a sand column experiment. Note the parallel between this and the corresponding dispersion of a tracer in a flowing river (Fig. 2-4). The same equation, with a correction factor for porosity in the case of the sand column, describes both situations. However, the physical processes responsible for the Fickian transport differ mechanical dispersion dominates in the sand column, while turbulent diffusion and the dispersion associated with a nonuniform velocity profile dominate in the river. 

Travel time and the longitudinal Fickian transport coefficient can also be evaluated from a continuous injection experiment, in which injection of tracer is initiated at time f=0 at a rate sufficient to establish a chemical concentration Co at the point of injection. Such an experiment is discussed for groimdwater in Section 3.2.5 the equation describing concentrations resulting from a continuous injection in a river is conceptually identical to Eq. (3.18). Equivalently, the injection of tracer can be described as mass per cross-sectional area per imit time (M), in which case the equation presented in the upper middle panel of Fig. 3.19 can also be used for a river, with porosity n equal to 1. 

In the absence of experimental tracer data, it is also possible to estimate Fickian transport coefficients from channel geometry and discharge. Equations for estimating these coefficients reflect the fact that lateral, or transverse, mixing is caused by turbulence (by definition there is no lateral advection in a river), whereas longitudinal mixing, while partly influenced by turbulence, is often caused primarily by variations in longitudinal water velocity in different parts of the charmel. 

---