On a family of mathematical models of adequate complexity, describing passive mass transfer in calm streambed flowes. (Russian. English summary) Zbl 1435.35306

Summary: The problems of modeling calm and shallow streambed flows of low turbidity within elongated and weakly curved sections are discussed. A technique based on the small parameter method of obtaining simplified mathematical models that adequately take into account the spatial nature of the flow is presented. In contrast to the widespread averaged models, the equations of mathematical models described in the article take into account the spatial structure of the flow, which allows us to study the influence of the shape of the bottom and coastline of the channel, as well as some external factors (for example, the wind) on the characteristics of mixing and distribution of matter in the stream.


35Q35 PDEs in connection with fluid mechanics
76R10 Free convection
76F10 Shear flows and turbulence
35R35 Free boundary problems for PDEs
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