Mathematical modeling and forecasting the dynamics of a segment of the river bed of Seversky Donets river

Abstract

The flow in the section of the Seversky Donets river in Kharkiv region is studied based on long-term measurements of the channel profile in a 10 cm increments. The geometry of the studied channel section on the Earth's surface has been determined by hydrological maps, and the cross-section profiles have been reconstructed by splines from the measurement results. The analysis of the results has revealed the profile variability in accordance with the change in the bottom sediments and the current year rainfall. A mathematical model describing the flow parameters in dependence on the slope and profile of the river channel has been developed. The model allows calculating flow velocities, dynamic pressure and viscous friction, predicting the evolution of coastal channel lines, the presence of stagnant zones with slow circulation, and predicting the dynamics of bottom drifts and channel overgrowing. Based on the three-dimensional flow of water in the channel with given geometry, numerical calculations by the finite element method are carried out. The flow rates are calculated and the presence of separated stagnant zones with slow circulation in which the channel overgrowth and water quality deterioration could be amplified is shown. Calculations of dynamic pressure and viscous friction shows the presence of areas with increased pressure which, in time, can ruin the riverbanks, contribute to the formation of bottom sediments, and increase the area of ​​stagnant zones with slow circulation. Since there is a system of positive feedbacks in the river ecosystem, the resulting deterioration in circulation and water quality cannot be stopped naturally and require special engineering and hydrogeological measures. The developed model allows planning various specific measures to prevent river erosion and overgrowth, to improve circulation and water quality by introducing the changes into the original geometric model as well as quantifying the changes caused by hydrodynamic factors that affect the evolution of the river system.