Investigating the celerity of propagation for small perturbations and dispersive sediment aggradation under a supercritical flow

The manuscript presents an investigation of the scales of propagation for sediment aggradation in an overloaded channel. The process has relevant implications for land protection, since bed aggradation reduces channel conveyance and thus increases inundation hazard; knowing the time needed for the aggradation to take place is important for undertaking suitable actions. Attention is here focused on supercritical flow, under which the process is dispersive and a depositional front cannot be clearly recognized; in these conditions, one needs to define propagation scales locally and instantaneously. Based on spatial and temporal rates of variation of the bed elevation we quantify a celerity of propagation for the sediment aggradation wave. Furthermore, considering that morphological processes are modeled by differential equations, the eigenvalues of the latter’s system are the celerities of the so-called small perturbations. With reference to a laboratory experiment with temporally and spatially detailed measurements, and after a review of existing approaches to determine the celerity of small perturbations considering or discarding the concentration of transported sediment, the manuscript shows how the celerities of propagation correlate with one another, while their values differ by orders of magnitude. It is argued that accounting or not for the solid concentration in the governing equations does not significantly impact the correlation trends, even one of the eigenvalues changes significantly. Finally, a bulk value of a dimensionless aggradation celerity is provided, that can serve as a rule-of-thumb estimation, useful for engineering purposes.