On a Family of Mathematical Models of Adequate Complexity, Describing Passive Mass Transfer in Calm Streambed
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.
Konstantin Nadolin, Cand. Sci. (Phys.–Math.), docent, Southern Federal University, 8-A, Milchakova St., Rostov-on-Don, 344090, Russian Federation, tel.: (863)2975285, e-mail: firstname.lastname@example.org
K.A. Nadolin. On a Family of Mathematical Models of Adequate Complexity, Describing Passive Mass Transfer in Calm Streambed Flowes. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 31, pp. 34-48. (in Russian) https://doi.org/10.26516/1997-7670.2020.31.34
mathematical model, streambed flow, turbulence, free surface, small parameter technique, passive admixture
1. Arguchintsev V.K., Arguchintseva A.V. Numeric modeling of flows and admixture transfer in stratified lakes. The Bulletin of Irkutsk State University. Series Mathematics, 2007, vol. 1, no. 1, pp. 42-51. (in Russian)
2. Babayan A.V., Nadolin K.A. Modeling of Substance Spreading in Two-Dimensional Flow of Viscous Fluid. Water Resources, 2000, vol. 27, no. 2, pp. 161-168.
3. Babayan A.V., Nadolin K.A. On modeling Taylor dispersion in a pipe of variable cross section. Bulletin of Higher Education Institutes. North Caucasus Region, Series Natural Sciences, 2001, no. 3, pp. 27-29. (in Russian)
4. Babayan A.V., Nadolin K.A. Modeling of scattering of matter in a three-dimensional open stationary flow of a viscous fluid. Bulletin of Higher Education Institutes. North Caucasus Region, Series Natural Sciences, 2001, Special Issue, Mathematical Modeling, pp. 23-25. (in Russian)
5. Vasil’ev O.F. Mathematical modeling of hydraulic and hydrological processes in water bodies and streams (a review of the work performed in the Siberian branch of the Russian Academy of Sciences). Vodnie Resursy, 1999, vol. 26, no. 5, pp. 600–611. (in Russian)
6. Zhilyaev I.V. Reduced models of hydrodynamics and mass transfer in channel flows. Cand. Sci. [Phys.-Math.] Diss.. Rostov-on-Don, 2018, 196 p. (in Russian)
7. Loitsyanskii L.G. Mechanics of Liquids and Gases. Pergamon Press Publ., 1966, 802 p. https://doi.org/10.1017/S0001924000056645
8. Monin, A.S., Yaglom, A.M. Statistical fluid mechanics. Cambridge, MIT Press Publ., 1979.
9. Nadolin K.A. On the Approach to Modelling of the Mass Transfer in River-bed Stream. Mat. Model., 2009, vol. 21, no. 2, pp. 14-28. (in Russian)
10. Nadolin K.A., Zhilyaev, I.V. A Reduced 3D Hydrodynamic Model of a Shallow, Long, and Weakly Curved Stream. Water Res, 2017, vol. 44, no.2, pp. 237-245. https://doi.org/10.1134/S0097807817020087
11. Knight D.W. River hydraulics - a view from midstream. J. Hydr. Res, 2013, vol. 51, no. 1, pp. 2-18. https://doi.org/10.1080/00221686.2012.749431
12. Stansby P.K. Coastal hydrodynamics - present and future. J. Hydr. Res, 2013, vol. 51, no. 4, pp. 341-350. https://doi.org/10.1080/00221686.2013.821678