Hydraulic resistance effect upon the dam-break functions

Abstract

The dam-break solution, a known centered simple-wave when resistance is neglected, is studied with the Chezy resistance formula added to the nonlinear shallow-water equations. Resistance transforms the wavefront from a characteristic curve into an envelope of charac-teristics. The flow near the tip differs from the other parts, due to a distinct boundary-layer type of region adjacent to the wavefront envelope. Then a perturbation leads to a system of partial differential equations with variable coefficients. Initial conditions are derived for the singularity at the origin. By studying its characteristic equations, this system is solved explicitly for the correction functions. Except at the tip, resistance raises the water surface and lowers velocities. These functions, no longer simple-waves, possess concurrent straight characteristic lines that map into another set of the same type. The critical flow locus moves downstream, faster for more resistance, and discharge rates are reduced. The method fails in the tip layer because the asymptotic expansions for the first derivatives lose validity there. Estimates are made indirectly for the wavefront velocity by observing where the boundary-layer effect becomes predominant.