Roll waves in a non-regular inclined channel

For nonlinear hyperbolic equations of a gas dynamic type with flow acceleration and friction terms, the classification of a special class of periodic travelling waves, which are known as roll waves, is given. As an illustration, the shallow water equations for the inclined channels of an arbitrary cross-section are considered. The analysis shows that the flow patterns depend upon the sign of the second derivative of the pressure function. The roll waves in regular channels with the convex pressure have the same structure as the waves described in Dressler [6]. For a nonconvex pressure function, the multi-jump configuration of roll waves is found.