Dynamic systems and optimal control

On a family of mathematical models of adequate complexity, describing passive mass transfer in calm streambed flowes

K. A. Nadolin

Southern Federal University, Rostov-on-Don, Russian Federation

Abstract: 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.

Keywords: mathematical model, streambed flow, turbulence, free surface, small parameter technique, passive admixture.

UDC: 519.63

MSC: 35Q35

Received: 28.10.2019

DOI: 10.26516/1997-7670.2020.31.34

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