The Hydraulic Geometry of Evolving Meandering Rivers

We study the bankfull hydraulic geometry of evolving meander bends. The analysis is driven by the recognition that none of the models introduced so far accounts for the conservation of the sediment mass, which leads to an unrealistic drop of the sediment transport capacity while the meander becomes longer. With this aim we propose a novel model to predict the adaptation of channel width and slope in evolving meanders, which is composed of a threshold relationship for the channel width and an ordinary differential equation for the slope, arising from an integral, meander-averaged formulation of the Exner equation. The latter accounts for three main processes: (i) meander elongation, (ii) width change, and (iii) bed aggradation due to reduction of the transport capacity. Our model predicts a reduction of both channel width and slope, whose magnitude is regulated by the parameter RT representing the ratio between the timescale of river planform and that of riverbed. When this ratio is large, the bankfull hydraulic geometry keeps nearly invariable; on the contrary, when RT is small, as channel sinuosity increases, the bankfull width and slope experience a significant change. Through remote sensing analysis and published data we provide estimates of the parameter RT for several meandering river reaches. We also trace the changes of the bankfull width of four dynamic meandering rivers in the Amazon basin by means of an innovative multitemporal bend-scale analysis. Observed evolutionary trajectories are satisfactorily reproduced by theoretical predictions.