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**Reduced 3D model of a passive admixture transport in shallow, elongated and weakly curved natural water-stream.**
*(English)*
Zbl 1469.86005

Faragó, István (ed.) et al., Progress in industrial mathematics at ECMI 2018. Proceedings of the 20th European conference on mathematics for industry, ECMI 2018, Budapest, Hungary, June 18–22, 2018. Cham: Springer. Math. Ind. 30, 111-116 (2019).

Summary: The main goal of the study is a validation of a simplified 3D mathematical model for passive admixture spreading in shallow flows. The tested model is oriented to the hydrological and ecological problems, and it can be applied to natural streams like rivers and channels. The earlier proposed model of the ‘elongated, shallow and weakly curved stream’ [K. A. Nadolin, Mat. Model. 21, No. 2, 14–28 (2009; Zbl 1177.76380)] takes into account the structure of a stream-bed for evaluation of flow velocity in every point of domain. This is a model advantage, which allows calculation of the admixture spreading in a channel with varying width and depth more accurately than by using in-depth averaged models. For example, we can observe the opposite flow in a near-surface zone, which may be caused e.g. by the wind. The results of numerical experiments show that this reduced 3D model adequately describes the admixture spreading processes in natural streams with acceptable accuracy.

For the entire collection see [Zbl 1467.00014].

For the entire collection see [Zbl 1467.00014].

### MSC:

86A05 | Hydrology, hydrography, oceanography |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |