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

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, 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. Later the analytical results are applied to three different turbulent flow situations: a dam break, the swash zone, and a tsunami runup.
The theoretical results yield simple explicit analytical expressions of the dam break wave with flow resistance. The results compare well with experimental data for both laminar and turbulent flow motion. The developments yield nice pedagogical applications of the Saint-Venant equations and method of characteristics. The simplicity of the equations may allow the extension of the method to more complex fluids.
Keywords : Dam break wave, Analytical solutions, Saint-Venant equation, Method of characteristics, Wave runup, Tsunami runup.

The Research Report is a refereed publication as part of the Hydraulic Model Report CH series published by the Department of Civil Engineering at the University of Queensland.