Analytical Study of Dam-Break Wave Tip Region

Abstract

A new method is proposed to solve the two-dimensional shallow-water equations and derive the hydraulic properties in the wave tip region of the dam-break flow on a dry frictional horizontal channel of a rectangular cross section. Based on the assumptions that the resistance coefficient remains constant and the velocity at the wave tip region is spatially uniform, a relation between the wave tip velocity and time is established. Theoretically, the present results apply to the entire dam-break duration because the calculated wave tip velocity never reduces to zero. With bottom resistance, the water depth at the transitional position increases, whereas the wave tip velocity decreases and the wave front position is significantly retarded as time passes. Taking into account that the wave tip velocity is about half of the positive wave front velocity without bottom resistance, the transitional position is identified to move first forward and then backward into the reservoir. Accordingly, the mass and momentum of the wave tip region increase monotonically with time. In addition, the temporal water surface profile in the wave tip region is presented.