RANS-based simulation of transverse turbulent mixing in a 2D geometry

Although transverse mixing is a significant process in river engineering when dealing with the discharge of pollutants from point sources or the mixing of tributary inflows, no theoretical basis exists for the prediction of its rate, which is indeed based upon the results of experimental works carried on in laboratory channels or in streams and rivers. The paper presents the preliminary results of a numerical study undertaken to simulate the transverse mixing of a steady-state point source of a tracer in a two-dimensional rectangular geometry, which is expected to reproduce a shallow flow. This geometry is that of Lau and Krishnappan (1977), who collected turbulent mixing data for a shallow flow. In the numerical study an approach based on the Reynolds Averaged Navier-Stokes (RANS) equations was applied, where the closure problem was solved by using turbulent viscosity concept. Particularly, the classical two-equations k-ε model was used. Two methods were applied to the model results to evaluate the turbulent transverse mixing coefficient. The effect on transverse mixing of a grid located upstream the tracer source was also studied. Numerical results were generally higher than the experimental data. This overestimation could be explained considering the hypothesis of isotropic turbulence underlying the k-ε model, which can lead to large turbulent viscosities and rate of mixing. However, RANS-based results may still be considered acceptable also providing the large uncertainties associated with literature predictive equations.