On steady alternate bars forced by a localized asymmetric drag distribution in erodible channels

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-Averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. This is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow-sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour-deposition patterns associated with the deployment of energy converters or other flow obstructions.