Modeling non-Fickian pollutant mixing in open channel flows using two-dimensional particle dispersion model

The non-Fickian particle dispersion model was developed in this study to model two-dimensional pollutant mixing in open channel flows. The proposed model represents shear dispersion using step-by-step arithmetic calculations, which consist of horizontal transport and vertical mixing steps, instead of using Fick's law. In the sequential calculations, the model directly applied the effect of vertical variations of both longitudinal and transverse velocities, whereas the Fickian dispersion model incorporates the effect of shear flow in the dispersion coefficients. Furthermore, in order to avoid the numerical diffusion errors induced by the grid tracking method of previously developed non-Fickian dispersion models, this model adopted the particle tracking technique to trace each particle. The simulation results in the straight channel show that the proposed model reproduced the anomalous mixing, which shows a non-linear increase of variance with time and large skewness coefficient in the initial period. However, in the Taylor period, the variance and skewness of the concentration curves approached the Fickian mixing. The simulation results in the meandering channel reveal that the proposed model adequately reproduced the skewed concentration–time curves of the experimental results whereas the Fickian dispersion model, CTM-2D, generated symmetrical curves. Further comparison between the simulation results and the tracer test results conducted in the Hongcheon River shows that the proposed model properly demonstrated the two-dimensional mixing without adopting Fick's law.