The evolution of a cross-channel trench under the influence of the transit hydrodynamic flow

The paper presents a river-bed mathematical model that is one-dimensional in space. In the model we use the original equilibrium formula of bed-load sediment motion, which takes into account the influence of bottom morphology, physical and mechanical parameters of the bottom material on bed-load sediment transport process is used. The formula does not contain new phenomenological parameters. The hydrodynamic flow is described by the steady motion equations within the bounds of the “shallow water” theory. The numerical algorithm for the solution of the governing equations by the control volume method is proposed. The problem of changing geometry of a cross-channel trench when moving over it transit hydrodynamic flow is considered as a verification of the model. The obtained solutions are compared with an experimental data and calculations of other authors. The movement front of the downstream and upstream trench regions, as well as the trench depth, are well-restored due to the model proposed. On average, we obtained a high degree of agreement between the numerical results and experimental data in the region, the mean-relative error between the calculated and measured data is close to 5 %. According to the verification results of the proposed model we have concluded that the mathematical model quantitatively and qualitatively describes the process of bottom surface deformation under the influence of hydrodynamic flow.