A stem spacing-based non-dimensional model for predicting longitudinal dispersion in low-density emergent vegetation

Abstract

Predicting how pollutants disperse in vegetation is necessary to protect natural watercourses. This can be done using the one-dimensional advection dispersion equation, which requires estimates of longitudinal dispersion coefficients in vegetation. Dye tracing was used to obtain longitudinal dispersion coefficients in emergent artificial vegetation of different densities and stem diameters. Based on these results, a simple non-dimensional model, depending on velocity and stem spacing, was developed to predict the longitudinal dispersion coefficient in uniform emergent vegetation at low densities (solid volume fractions < 0.1). Predictions of the longitudinal dispersion coefficient from this simple model were compared with predictions from a more complex expression for a range of experimental data, including real vegetation. The simple model was found to predict correct order of magnitude dispersion coefficients and to perform as well as the more complex expression. The simple model requires fewer parameters and provides a robust engineering approximation.

The Impact of Cylinder Diameter Distribution on Longitudinal and Transverse Dispersion Within Random Cylinder Arrays

“…Sonnenwald et al. (2019a) suggested non‐dimensionalizing by cylinder spacing instead of cylinder diameter as the characteristic mixing length. Figure 10 shows that D x / Us and D y / Us both collapse reasonably well onto a single line, again removing any evidence of cylinder diameter non‐uniformity effects.…”

“…(2019). For the remaining studies, s has been estimated using Equation (Sonnenwald et al., 2019a; Tanino & Nepf, 2008): $$$\begin{array}{l}s\approx d\sqrt{\frac{1+2\phi }{4\phi }-\sqrt{\pi }\sqrt{\frac{1-2\phi }{4\phi }}\left(\frac{1-\text{erf}(\sqrt{4\phi /(1-2\phi )})}{\mathrm{exp}(-4\phi /(1-2\phi ))}\right)-1}\hfill \end{array}$$$ …”

“…With respect to the longitudinal dispersion coefficient, D x , Sonnenwald et al. (2019a) presented laboratory data relating to three different arrangements of artificial emergent vegetation. One arrangement comprised randomly‐distributed 8 mm diameter cylinders, ϕ = 0.027, tested at Re d = 450.…”

“…We then utilize the analysis presented by Sonnenwald et al. (2019a) to validate our model predictions of the longitudinal dispersion coefficient.…”

“…The first is based on a qualitative comparison with the laboratory flow-field measurements presented by Ricardo et al (2014). We then utilize the analysis presented by Sonnenwald et al (2019a) to validate our model predictions of the longitudinal dispersion coefficient. Prior to discussing the comparisons between the measured and modeled data sets, it is important to note the following aspects.…”