Keywords: 
• environmental hydraulics /
• rivers /
• advection-diffusion /
• classification of width /
• the criterion of discrimination

Abstract: The analytical solution for advection-diffusion equations exists in different forms depending on the solution conditions. The river width class is an important parameter for choosing a solution for calculating the pollutant diffusion rate in rivers due to pollution discharge. However, it would be difficult to implement such a guiding principle in practical applications due to lack of specific criteria for classification of river width. In accordance with the level of river pollutions affected by boundary reflectivity and the result of the consideration of simplified conditions for analytical solutions of advection-diffusion equations, we propose a river width as wide, medium, and narrow three categories. The criteria for classification of river width and the corresponding method of classification are presented. The mathematical expressions for the identification of the three categories are also deduced. The influence of boundary reflection is usually negligible for 2-D river flow and the mixing length in a well-mixed cross section is less or equal to the river width. These conditions are used to solve the advection-diffusion equations for the three categories. The critical dividing line is obtained for separating the wide category from medium and narrow ones. While, the similar line for separating the medium category from the narrow ones is also derived. Finally, it is important to point out that the classified wide, medium, and narrow three categories are relative to each other. Different results could be obtained in the different hydraulic elements, diffusion coefficients, sewage strengths and allowable pollutant concentrations in the same river.