Modeling of channel processes in a channel cross section

An erosion mathematical model of a sand channel coastal slope, which occurs under the influence of passing flood wave, is formulated. The model includes the equation of motion of a quasi-steady hydrodynamic flow in the channel section. The movement of the bottom and bank surface of the channel is determined from the solution of the Exner equation, which is closed by an original analytical model of the movement of traction sediments. The model takes into account transit, gravitational and pressure mechanisms of movement of bottom material, and does not contain phenomenological parameters. The movement of the free surface of a hydrodynamic flow is determined from the interpolation of experimental data. The model takes into account changes in the average turbulent viscosity along the alignment when the channel alignment changes. The influence of quasi-steady hydrodynamic flow on mass loss in the channel section was studied. A criterion has been introduced to determine the disequilibrium of the channel flow. It is shown that to model channel deformations in this case, it is necessary to take into account a non-zero gradient of sediment movement along the channel axis. Numerical calculations have been carried out demonstrating the qualitative and quantitative influence of these features on the process of determining the turbulent viscosity of the flow and the erosion of the coastal slope of the channel. Data comparison on coastal deformations obtained as a result of numerical calculations with known flume experimental data showed their good agreement.