Modelling of Water Erosion and Accumulation Processes along the Longitudinal Profiles of Ukrainian Carpathian Rivers

The results of computer modelling of the critical flow velocity of rivers in the Ukrainian Carpathians are presented in the article. In cooperation with the Department of Applied Mathematics of Ivan Franko National University, Lviv, a highly specialized module for visualization of erosive and accumulative processes in the Carpathian rivers was developed. The erosion–accumulation model is implemented in the Microsoft Visual Studio Express integrated environment in C++ using the Open Graphics Library graphics-programming tool. The modelling is based on the theory of critical flow velocity. The velocity on an inclined plane was simulated, the value of which was automatically calculated on each section of the profile relative to the velocity on the horizontal plane. The flow velocity and the angle of inclination affect the erosional and accumulative activities of rivers, the correlation between which have different parameters along their longitudinal profile. The flow velocity modelling was conducted interactively on the longitudinal profiles of rivers such as the Borzhava, Bystrytsia Nadvirnianska, Dniester (mountain section), Latorytsia, Lymnytsia, Prut, Rika, Stryi, Svicha, Tereblia, Teresva, and Tysa (mountain section). In the upper sections of the profile, where the slope is steep, rapid flow leads to predominant erosion. The potential for erosion begins on sections with a slope of 20–30% at a flow velocity of 1.7 m/s, while on sections with a slope of 3–10%, it occurs at a velocity of 1.8 m/s. It should be considered that the flow force in the upper sections is low because of its low water content, but the inclination of the river’s fall is significant, and a rather high velocity is required to dislodge rock particles from the bed. In the middle and lower river reaches, the water content of the rivers is much higher, but the flow inclination is small, so a velocity is slightly higher than in the river upper reaches is required to initiate erosion. The transport of solid material is common in the most concave parts of the profiles. Sediment accumulation prevails in the lower sections of the profiles, where the curve is close to the horizontal (3-10о). The developed model partially explains the varying erosional and accumulative activity of rivers of mountain type and has scientific, cognitive and practical importance.