The Hydraulic Geometry of Evolving Meandering Rivers

Abstract

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.

Adjustment of self‐formed bankfull channel geometry of meandering rivers: modelling study

“…The result suggests that bank erodibility, which can in turn affect the lateral migration rate, is sufficiently high so that longitudinal adjustment, which is primarily dominated by streamwise variation in sediment transport rate, cannot keep pace. This result is in accord with previous studies (Simon and Darby, 1997;Monegaglia and Tubino, 2019).…”

“…The difference in these two timescales has also been addressed in terms of bank erodibility. Monegaglia and Tubino (2019) found through their meander bend scale analysis that if the timescale ratio between planform evolution, which is predominantly controlled by bank erodibility, and riverbed slope evolution is large, bankfull channel geometry remains relatively constant as a meander loop develops. This is because the slope adjustment due to channel meander elongation takes place so slowly that the reach is able to maintain near equilibrium in sediment transport.…”

“…Such a model can be used, for example, to examine the difference in adjustment timescale of the longitudinal profile, as well as that of the cross‐sectional profile (i.e., width and depth). Previous studies have addressed the difference in these two adjustment timescales (e.g., Schumm, 1991; Simon and Darby, 1997; Monegaglia and Tubino, 2019). These studies have, however, targeted straight channels, both banks of which are considered to exhibit the same processes (Simon and Darby, 1997) or have been focused on the scale of a meander bend (Monegaglia and Tubino, 2019).…”

“…Previous studies have addressed the difference in these two adjustment timescales (e.g., Schumm, 1991; Simon and Darby, 1997; Monegaglia and Tubino, 2019). These studies have, however, targeted straight channels, both banks of which are considered to exhibit the same processes (Simon and Darby, 1997) or have been focused on the scale of a meander bend (Monegaglia and Tubino, 2019). Timescales of longitudinal and cross‐sectional profile adjustments of meandering streams at larger temporal and spatial scale are, therefore, yet to be investigated.…”

A Cusp Catastrophe Model for Alluvial Channel Pattern and Stability

“…The interrelationships between the (1) oncoming bed material load and the sediment carrying capacity of the flow, and (2) the erodibility of the river banks and the erosive power of the water decide essentially the general direction of the self-adjustment. Besides a variety of available methods for predicting channel stability parameters, a point of high research interest is the effect of hydraulic parameters and factors, such as the discharge, median grain size, Shields parameter, vegetation type, average roughness, and sediment composition [28][29][30][31][32]. On the basis of the preliminary analysis of the multitude of parameters reported in the literature, the synthetic indexes of river-bed stability determined by the longitudinal river-bed stability in contrast to the transverse river-bed stability are adopted in this study, the longitudinal index of B.и.AcrpaxaниeB, and the transverse index of C. T. Aлтунинare expressed in the form [27]:…”