Abstract
In this study, two types of particle tracking models were presented to investigate the applicability in the two-dimensional solute mixing simulations. The conventional particle tracking model, denoted as PTM, was developed based on Fick’s law, which adopted the dispersion coefficient to calculate the random displacements. The other model is the particle dispersion model (PDM), which computes the shear dispersion process by dividing into two computation procedures as the shear translation and the vertical mixing. The PTM and the PDM included the effects of vertical profiles of velocity in the computation of dispersion coefficients and the shear translation step, respectively. The main difference between the two models is whether the shear dispersion process is reproduced using Fick’s law or the direct computation method. These differences were clearly revealed by comparing with the analytic solution of the advection-dispersion equation. The concentration curve resulting from the PTM shows the Gaussian curves, which were well-fitted with the analytic solution in both initial and Taylor periods. Meanwhile, the PDM presented skewed curves in the initial period and gradually turned to the symmetric shape in the Taylor period. The inherent differences of the two particle tracking models were scrutinized against the two-dimensional tracer test results, which show the non-Fickian mixing properties. The comparisons of concentration–time curves reveal that the PDM reproduced a more accurate shape of the curves than the results by the PTM by demonstrating skewed concentration curves.
Highlights
The increase of urban and industrial areas become a threat to aquatic environments by increasing possibilities of water pollution
The simulation results of the two particle tracking models were validated by comparing with the analytic solution of the advection-dispersion equation
The results by the skewedsolution concentration initial period, and the wereThese gradually fitted to the fitted to show the analytic aftercurves t = 30 in s, the as reported by Park andresults results show the analytic solution after t = 30 s, as reported by Park and Seo [31]. These results show the distinct distinct differences between the two models, where the Particle Tracking Model (PTM) derives the results by assuming a differences between the two models, where the PTM derives the results by assuming a complete complete balance between the shear advection and the vertical diffusion, whereas the particle dispersion model (PDM) directly balance between the shear advection and the vertical diffusion, whereas the PDM directly calculates calculates the process of achieving the balance
Summary
The increase of urban and industrial areas become a threat to aquatic environments by increasing possibilities of water pollution. The 2D mixing can be described based on the shear dispersion theory, as described, in which a pollutant cloud is stretched by shear flows in the longitudinal and transverse directions, and simultaneously diffused through flow depth by the turbulent diffusion [3]. In the 2D mixing model, the shear dispersion theory is modeled using Taylor’s study [4], in which the mass flux. Water 2020, 12, 3535 the mass flux term derived from the depth-averaging process is assumed to be proportional to the concentration gradient based on Taylor’s assumption as follows [5]. Term derived from the depth-averaging process 1 h is assumed. D gradient based on Taylor’s assumption as follows [5].
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