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Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froudenumber F < 2, we categorize completely the existence and convective stabilityof hydraulic shock profiles of the Saint Venant equations of inclined thin-filmflow. Moreover, we confirm by numerical experiment that asymptotic dynamics forgeneral Riemann data is given in the hydrodynamic instability regime by eitherstable hydraulic shock waves, or a pattern consisting of an invading roll wavefront separated by a finite terminating Lax shock from a constant state at plusinfinity. Notably, profiles, and existence and stability diagrams are allrigorously obtained by mathematical analysis and explicit calculation.

Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow