×

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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76R10 Free convection
76F10 Shear flows and turbulence
35R35 Free boundary problems for PDEs
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[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, 1, 42-51 (2007)
[2] Babayan, A. V.; Nadolin, K. A., Modeling of Substance Spreading in Two-Dimensional Flow of Viscous Fluid, Water Resources, 2, 161-168 (2000)
[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, 3, 27-29 (2001)
[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, 23-25 (2001)
[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, 5, 600-611 (1999)
[6] Zhilyaev, I. V., Reduced models of hydrodynamics and mass transfer in channel flows, Cand. Sci. [Phys. -Math. ] Diss., 196 (2018)
[7] Loitsyanskii, L. G., Mechanics of Liquids and Gases, 802 (1966), Pergamon Press Publ. · Zbl 0247.76001
[8] Monin, A. S.; Yaglom, A. M., Statistical fluid mechanics (1979), Cambridge, MIT Press Publ.
[9] Nadolin, K. A., On the Approach to Modelling of the Mass Transfer in River-bed Stream, Mat. Model., 2, 14-28 (2009) · Zbl 1177.76380
[10] Nadolin, K. A.; Zhilyaev, I. V., A Reduced 3D Hydrodynamic Model of a Shallow, Long, and Weakly Curved Stream, Water Res, 2, 237-245 (2017)
[11] Knight, D. W., River hydraulics - a view from midstream, J. Hydr. Res, 1, 2-18 (2013)
[12] Stansby, P. K., Coastal hydrodynamics - present and future, J. Hydr. Res, 4, 341-350 (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.