333 2009,21(3):333-340 DOI: 10.1016/S1001-6058(08)60153-5 SIGMA-COORDINATE NUMERICAL MODEL FOR SIDE-DISCHARGE INTO NATURAL RIVERS * LIU Zhao-wei, CHEN Yong-can, LI Ling State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China, E-mail: liuzhw@tsinghua.edu.cn ZHENG Jing-yun Wenzhou Oujiangkou Development and Construction Headquarters, Wenzhou 325027, China (Received June 16, 2007, Revised October 22, 2007) Abstract: Due to large topography slopes in natural rivers, pollutant concentration embodies a property of three-dimensional distribution when wastewater is discharged from effluents along the bank. With the sigma coordinate along the vertical dimension fitted to both the moving free surface and the bed topography, a three-dimensional numerical model was developed in the present work to address pollutant transport processes in the above-mentioned cases. To avoid the reduction in accuracy caused by spurious diffusion in the case of steep bottom slopes, a formula for horizontal diffusion in the sigma coordinate system was derived. A case study for the side discharge into a straight open-channel flow shows that numerical results are verified well by experimental data. Furthermore, the present model is also verified by the simulation of discharging wastewater from Fuling Phosphorus Factory effluent into the Three Gorges Reservoir and the agreement between the numerical simulation results and field observation data is satisfactory. The change of the mixing zone scope in the water surface versus the layers along the vertical dimension was also discussed in detail. The study shows that a more realistic calculation for pollutant discharge has been provided by the present model than by the depth-average model which predicts an unrealistically smaller mixing zone. Key words: sigma-coordinate, three-dimensional model, side-discharge, natural rivers 1. Introduction In the prediction of mixing zones in a natural river, two-dimensional models have been commonly used with a simpler structure and higher computational efficiency. For example, with a depth-averaged finite element model, Jiang [1] simulated the concentration distribution in the region near the Taohuaxi effluent which discharges wastewater into the Three Gorges Reservoir, and Qi [2] investigated pollutant transport processes discharged from a effluent by means of hierarchy grids in a * Project supported by the National Basic Research and Development Program of China (973 Program, Grant No. 2006CB403304). Biography: LIU Zhao-wei (1973), Male, Ph. D., Lecturer two-dimensional domain. However, mixing zone predicted with the two-dimensional model is generally smaller than the actual size, because the pollutant concentration shows a three-dimensional distribution in the region adjacent to an effluent due to large topography slopes in the natural river. Consequently, three-dimensional models became the focus of some researchers. With the horizontal multi-layer three-dimensional model, Chen [3] predicted the mixing zones resulted by the Fuling Phosphate Fertilizer Factory effluent discharging wastewater into the Yangtze River. However, the water column in the shallow region near the effluent was represented by only one layer and thus the three-dimensional feature of concentration could not be predicted accurately. The sigma-coordinate model is another major form to solve the shallow water equations [4-10] . In this