Morphodynamic reaction of a schematic river to sediment input changes: Analytical approaches

The paper investigates the morphodynamic reaction of a schematic river to a perturbation of the sediment input imposed at its upstream end. The consequent evolution of the initially equilibrium river can be studied by means of various models (0-dimensional; 1-D parabolic and 1-D hyperbolic with uniform sediments; 1-D hyperbolic with graded sediments), depending on the more or less simplified differential equations applied for describing the water and sediment motion.The paper discusses a number of analytical solutions obtained with two types of boundary conditions, namely: (i) stepwise change of the sediment input, very often connected to anthropogenic actions, and (ii) sinusoidal input variation with prescribed period, typically associated to the meteorological cycles (short period) or to the geological and climate change (long period). The solutions provide an explicit expression for the Response Time of the river for the condition (i) and the Attenuation Length of the river for the condition (ii). The two quantities as defined in this paper do have a specific physical meaning, strictly connected with the corresponding boundary conditions, which measures the reactivity of the river to external disturbances.A comparative application of the analytical solutions to various (prevalently large) rivers of the world is given, together with a final discussion.