ARTICLE Transverse mixing of pollutants in streams: a review H. Sharma and Z. Ahmad Abstract: Spilling or release of foreign particles in the flowing water is considered as pollution of water, and due to the inherent property of water to dissolve the substance, the particulate is well mixed in water. To monitor the extent of pollution in a stream it is essential to know how the pollutants mix in the river. It is observed that vertical mixing of pollutants is a very rapid process in the vertical directions and longitudinal mixing occurs very far from source of pollutant, which is generally out of reach of observations. Thus intermediate or transverse mixing zone is considered very important for water quality modeling. This paper is an attempt to summarize the phenomenon behind pollutant transport, reduction of three-dimensional advection–dispersion equation to two-dimensional equation, and factors causing and affecting transverse mixing of pollutants. Key words: river mixing, transverse mixing, secondary currents, advection–dispersion equation, numerical models. Résumé : Le déversement ou l’émission de particules étrangères dans l’eau mouvante est considéré comme une pollution de l’eau et, en raison de la propriété inhérente de l’eau de dissoudre des substances, les particules sont bien mélangées dans l’eau. Pour surveiller l’étendue de la pollution dans un ruisseau, il est essentiel de connaître la manière dont les polluants se mélangent dans la rivière. Il a été remarqué que le mélange vertical des polluants est un processus très rapide et que le mélange longitudinal survient très loin de la source de pollution, laquelle est généralement hors de portée des observations. La zone de mélange intermédiaire ou transversal est considérée comme étant très importante pour la modélisation de la qualité de l’eau. Le présent article se veut une tentative de résumer le phénomène a ` la base du transport des polluants, la réduction de l’équation tridimen- sionnelle d’advection–dispersion a ` une équation bidimensionnelle et les facteurs causant et affectant le mélange transversal des polluants. [Traduit par la Rédaction] Mots-clés : mélange en rivière, mélange transversale, courants secondaires, équation advection–dispersion, modèles numériques. Introduction Water is a source for many industrial and domestic needs, which include from drinking to cooling of reactors. Need of pure water for these tasks, is as important as management of water quality. When accidents happen and pollutants are spilled into the water, they get mixed in the water and pollute it. Understand- ing the mechanism of mixing of pollutants is necessary for the management of pollutants control in streams. When any pollut- ant is spilled into the river, due to the dominance of vertical turbulence and least dimension of any river system, the pollutant gets mixed along the depth very quickly. The process of the pol- lutant getting mixed along the depth is termed as vertical mixing and longitudinally it spreads up to 50–100 times of the depth (Yotsukura and Sayre 1976). After getting mixed into the vertical direction under the action of transverse turbulence and variation in vertical profiles of transverse velocity, pollutant starts to spread along the river width and mixes along the cross section of the river. This transverse spreading and mixing of pollutant under the action of transverse shear and turbulence is termed as transverse mixing. If the source of pollutant is unsteady in nature, due to which pollutant further travels downstream under the action of longitudinal gradients and this mixing of pollutant under the action of longitudinal gradients is termed as longitudinal mixing. As the vertical mixing is a very rapid process and is dominant near the source of pollutant spill, whereas the longitudinal mixing is of importance very far from the source so that it makes it unimportant to model for environmental concern. This paper is a compendium regarding various processes involved in pollutant mixing in a river and the process of transverse mixing and factors affecting it. Physical processes of pollutant transport If a small quantity of any tracer like dye is injected into the river, the tracer cloud not only changes its shape but also in- creases in the volume at the same time as it is carried away down- stream by the stream flow. The phenomenon of transport and dye tracer mixing involves various physical processes, which are clas- sified as advection, diffusion, and dispersion. These processes will be discussed briefly. Advection Advection can be defined as the process where tracer cloud moves bodily in the flowing stream under the action of imposed current. Advection helps in transporting any dissolved or sus- pended tracer away from the fixed source in the downstream, hence showing that it is an important phenomenon to be consid- ered while modeling the transport of pollutant in the flowing media. To quantify the intensity of advection, the term advective flux is defined as follows (Fischer et al. 1979; Elhadi et al. 1984; Rutherford 1994): “The amount of tracer/substance transported per unit time per unit area perpendicular to the current is termed as advective flux and is the product of velocity and transported concentration of tracer/substance.” Mathematically, advective flux can be formulized as (Elhadi et al. 1984): (1) T ad = UC Received 19 December 2013. Accepted 15 March 2014. H. Sharma and Z. Ahmad. Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247 667, India. Corresponding author: Himanshu Sharma (e-mail: smile4anshu@gmail.com). 472 Can. J. Civ. Eng. 41: 472–482 (2014) dx.doi.org/10.1139/cjce-2013-0561 Published at www.nrcresearchpress.com/cjce on 31 March 2014. Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by UTSA LIBRARIES on 09/11/14 For personal use only.