River mixing—A state-of-the-art report

Abstract

This report is intended as a reference for practising engineers. A description of the various physical processes involved in the spreading of a substance in river flows as well as the mathematical formulation of these processes is given. These processes are combined in the mass balance equation to describe the mixing of substances released into rivers. The difficulties of solving three-dimensional mixing problems for real river situations are discussed. The simplification of the equation into two dimensions using depth averaging and the introduction of the stream-tube concept are described. Analytical and numerical solutions are recommended. The conventional Fickian description of one-dimensional mixing is given, followed by the description of a model that takes into account the non-Fickian behaviour often observed. Sample problems of one-dimensional and two-dimensional mixing are solved, using the recommended procedures. The effects of ice cover on mixing are discussed and cases of nonconservative substances are described. Key words: mixing, rivers, dispersion, concentration distribution, longitudinal mixing, transverse mixing, stream-tube model.