Dam-break waves in power-law channel section

The aim of this work is to highlight the effects of cross-sectional shape on dam-break wave propagation along channels by the solution of 1D conservative equations assuming a power-law variation of the channel width. An exact Riemann solution that allows a second-order accuracy of the solution for the power-law section shape is provided and is applied to the dam-break problem in valleys with different shapes but the same dam area. The streamflow state variables upstream of the bore and the bore speed for some typical sectional shapes (rectangular, triangular, concave, and convex banks) are determined as functions of variable flow depth differences and of the power law index.