Simplified three-dimensional mathematical models of hydrodynamics and passive mass transfer in calm channel flows

In this work, we discuss problems of modeling calm channel flows of low turbidity on long, slightly curved watercourses. We present simplified mathematical models obtained by the method of a small parameter from the Reynolds equations for incompressible fluids closed by the Boussinesq hypothesis and the diffusion equations of decaying matter in a moving medium. Within the framework of this approach, we propose a classification of channel flows. In contrast to the common averaged equations, the models proposed take into account the spatial structure of the flow, which makes it possible to study the influence of the channel shape and some external factors (for example, wind effects) on the mixing and distribution of matter in the flow.