Applications of the Saint-Venant Equations and Method of Characteristics to the Dam Break Wave Problem

Surge waves resulting from dam breaks have been responsible for numerous losses. Modern predictions of dam break wave rely too often on numerical predictions, validated with limited data sets. Despite a few studies, there has been a lack of basic theoretical and physical studies for the past 40 years. Current knowledge of dam break wave surging down rough surfaces remains rudimentary, while there is still some arguments of the flow fundamentals. The present work is focused on simple solutions of the dam break wave problem using the Saint-Venant equations and the method of characteristics. Analytical solutions are developed for an instantaneous dam break with a semi-infinite reservoir in a wide rectangular channel. After a review of well-known solutions, further ideal-fluid flow solutions are detailed. These include ideal dam break wave flow on horizontal and sloping channels, with or without initial flow motion. The effect of the presence of water in the downstream channel is discussed. New analytical solutions of dam break wave of real fluids are developed for turbulent flow (Section 4.) and laminar flow motion (Section 5.). These simple theoretical developments include the break wave in horizontal channels with bed friction, dam break wave with initial flow motion, and dam break waves on flat slope channels with bed friction and initial flow motion. The analytical results were validated by successful comparisons between theoretical results and several experimental data sets obtained in large-size facilities. Later the analytical results are applied to three different turbulent flow situations: a dam break, the swash zone, and a tsunami runup. The advantages of the present developments are five-fold. First the theoretical results yield simple explicit analytical expressions of the dam break wave with flow resistance. The theoretical results compare well with experimental data and with more advanced theoretical solutions. They include both laminar and turbulent flow motion. Second the developments are simple, and they yield nice pedagogical applications of the Saint-Venant equations and method of characteristics that are wellsuited to undergraduate teaching of hydraulic engineering. Third the analytical solutions may be used to validate numerical solutions of the method of characteristics applied to the dam break wave problem. Fourth the development is applied to a wide range of flow conditions, including the effects of bed slope and initial flow motion. This yields a wide range of practical applications. Fifth the simplicity of the equations may allow the extension of the method to more complex fluids (e.g. non-Newtonian fluids). It is however acknowledged that the present approach is limited to semi-infinite reservoir, rectangular channel and quasi-instantaneous dam break