The form of a monoclinic wave propagating along an initially dry riverbed

The problem of the propagation of a flood release wave in an initially dry wide rectangular riverbed with a constant slope and a bottom roughness is considered. Flood release waves occur in the tails of hydroschemes during the passage of high floods, as well as during short-term regulation of water course for energetics, irrigation, etc. The main method for problem solving on the propagation of flood release waves in riverbeds is mathematical modeling on the basis of differential equations for the streamflow - the Saint-Venant equations, using numerical methods. Analytical solutions of the Saint-Venant equations can be constructed only in rare cases. Nevertheless, these solutions are of great interest, since they are important tests for numerical methods. Comparison of the results of the numerical experiment and the analytical test showed a very good agreement, which gives grounds to recommend the applied technique for widespread use.