Center for Complex and Nonlinear Science

Analysis of an evolution model for a river channel shows how three types of shocks determine the profile of the channel. This model shows that in a young river channel, evolution is driven by white noise magnifying into a bore followed by a hydraulic jump. This mechanism produces a convex profile typical of young landscapes. A small knick-point then develops at the bottom of the unstable convex profile. This knick-point is magnified and colored into a diffusive shock which travels upslope, digging into the convex profile until the profile becomes concave, typical of mature landscapes.