Movement of sediment over periodic bed

The movement of bed load along the closed conduit can lead to a loss of stability of the bed surface, when bed waves arise at the bed of the channel. Investigation of the development of bed waves is associatedwith the possibility of determining of the bed load nature along the bed of the periodic form. Despite the greatattention of many researchers to this problem, the question of the development of bed waves remains open at thepresent time. This is due to the fact that in the analysis of this process many researchers use phenomenologicalformulas for sediment transport in their work. The results obtained in such models allow only assess qualitatlythe development of bed waves. For this reason, it is of interest to carry out an analysis of the development ofbed waves using the analytical model for sediment transport.
The paper proposed two-dimensional profile mathematical riverbed model, which allows to investigate the movement of sediment over a periodic bed. A feature of the mathematical model is the possibility of calculatingthe bed load transport according to an analytical model with the Coulomb – Prandtl rheology, which takes intoaccount the influence of bottom surface slopes, bed normal and tangential stresses on the movement of bedmaterial. It is shown that when the bed material moves along the bed of periodic form, the diffusion and pressuretransport of bed load are multidirectional and dominant with respect to the transit flow. Influence of the effectsof changes in wave shape on the contribution of transit, diffusion and pressure transport to the total sedimenttransport has been studied. Comparison of the received results with numerical solutions of the other authors hasshown their good qualitative initiation.