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

The paper 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 the celerity of propagation for the sediment aggradation wave. Furthermore, considering that morphological processes are modeled by a system of differential equations, the eigenvalues of the latter are the celerities of the so-called small perturbations. After a review of existing approaches to determine the celerity of small perturbations, taking into account or discarding the concentration of transported sediment, the paper considers a laboratory experiment with temporally and spatially detailed measurements, whose results are representative of those of several others performed in the same campaign. The relationships between the local and instantaneous Froude number, the celerity of small perturbations, and the celerity of the aggradation wave are explored. The celerity of the aggradation wave is correlated to that of the small perturbations, while their values differ by orders of magnitude. Our results indicate that accounting or not for the solid concentration in the governing equations does not significantly impact the correlation between the two types of celerity, even if one of the eigenvalues changes significantly in value. Finally, the aggradation celerity is generally below 0.05 times the initial flow velocity, with this serving as a rule-of-thumb estimation that may be useful for engineering purposes.