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Some self‐similar solutions in river morphodynamics

Aggradation and degradation in one‐dimensional channels are often modeled with a simplified nonlinear diffusion equation. Different degrees of nonlinearity are obtained using the Chezy and Manning/Gauckler‐Strickler laws for the friction coefficient combined with a sediment transport equation having a generalized form of the Meyer‐Peter and Müller formula. Analytical self‐similar solutions for the “dam break” and the base‐level lowering are presented. While the linear case corresponds to the classic diffusion equation, the main effect of the nonlinearity appears to be the presence of singularities in the self‐similar solutions, related to the finite speed of propagation of perturbations.