On the wave-front shape and the advancing of the wetting front of a dam-break flood over an inclined plane of arbitrary bottom slope

In this note we consider the analysis of the wave-front shape resulting from the sudden release of a finite volume of water over an inclined plane bed of arbitrary bottom slope. To that end we use the one-dimensional turbulent shallow water equations with a constant friction factor. We propose an asymptotic analytical solution for the height and velocity in the wave tip region based on the velocity of the wetting front and its temporal derivatives, in a similar fashion as Whitham (1955). For large time, an analytical solution is obtained for the advance of the wetting front. This proposal is compared and validated with a numerical simulation computed with a second-order TVD-MinMod numerical scheme. The divergence of the Hunt’s solution (Hunt 1982; Hunt 1984) for the advancing of the wetting front as time increases is also established. Our solution for the tip region is tested against the numerical one, and is also compared with that deduced by Hunt (1984) for small slopes of the bottom - a really good agreement is found.