An exact solution for ideal dam-break floods on steep slopes

The shallow‐water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well‐suited for testing the robustness and accuracy of numerical models used to model shallow‐water flows on steep slopes.