Sediment load determines the shape of rivers

Abstract

Understanding how rivers adjust to the sediment load they carry is critical to predicting the evolution of landscapes. Presently, however, no physically based model reliably captures the dependence of basic river properties, such as its shape or slope, on the discharge of sediment, even in the simple case of laboratory rivers. Here, we show how the balance between fluid stress and gravity acting on the sediment grains, along with cross-stream diffusion of sediment, determines the shape and sediment flux profile of laminar laboratory rivers that carry sediment as bedload. Using this model, which reliably reproduces the experiments without any tuning, we confirm the hypothesis, originally proposed by Parker [G. Parker, J. Fluid Mech. 89, 127–146 (1978)], that rivers are restricted to exist close to the threshold of sediment motion (within about 20%). This limit is set by the fluid–sediment interaction and is independent of the water and sediment load carried by the river. Thus, as the total sediment discharge increases, the intensity of sediment flux (sediment discharge per unit width) in a river saturates, and the river can transport more sediment only by widening. In this large discharge regime, the cross-stream diffusion of momentum in the flow permits sediment transport. Conversely, in the weak transport regime, the transported sediment concentrates around the river center without significantly altering the river shape. If this theory holds for natural rivers, the aspect ratio of a river could become a proxy for sediment discharge—a quantity notoriously difficult to measure in the field.

A width‐based approach to estimating historical changes in coarse sediment fluxes at river reach and network scales

“…As posited by Popović et al (2021) on the grounds of experiments on bedload‐dominated laboratory rivers (Abramian et al, 2020), an increase in sediment discharge progressively widens a river. The results of physical models of coarse‐bedded channels indicated that the reach‐averaged active channel width is positively correlated with the bedload transport rate (Peirce et al, 2018), clearing the way for the supposition that the active width and its variations can be adopted as parameters for estimating changes in coarse sediment fluxes.…”

“…Currently, pinpointing a direct association between the width of a river's active channel and the absolute values of sediment fluxes occurring at a given reach (e.g., expressed bed material load volume) is infeasible because this relationship is influenced by numerous river features (e.g., sediment grain size, transport capacity, morphological configuration) (e.g., Mueller & Pitlick, 2013, 2014). That said, Popović et al (2021) recently hypothesized that the shape of a river can be used as a proxy for sediment discharge. Peirce et al (2018) also demonstrated in a flume experiment that variations in the active channel width are positively correlated with changes in coarse sediment transport.…”

“…Correspondingly, the aim of the present work was to verify whether the relationship that Peirce et al (2018) found in a laboratory is equally applicable to actual rivers. We took on this task because, partially following the hypothesis of Popović et al (2021), this would allow us to explore variations in the active channel width as a reliable proxy for sediment flux changes. On the basis of the aforementioned relationships between the bed material load and features of an alluvial channel, we focused our investigation on coarse‐bedded and unconfined alluvial channels, for which a positive correlation between changes in the active channel width and coarse sediment fluxes was previously demonstrated in laboratories (Abramian et al, 2020; Peirce et al, 2018).…”

“…Variations in the width of the active channel in a coarse‐bedded river can be related to changes in local sediment supply and bedload transport (Bertrand & Liébault, 2019; Jacobson & Gran, 1999; Liébault & Piégay, 2002). On the basis of results obtained from laboratory rivers (Abramian et al, 2020), Popović et al (2021) concluded that the shape of a river, expressed in terms of channel width and depth, strongly depends on its sediment discharge. Furthermore, flume experiments conducted by Peirce et al (2018) uncovered, through a positive correlation, that variations in the width of an active channel are quantitatively associated with changes in bedload transport.…”

Erosion of cohesive grains by an impinging turbulent jet

“…A large part of the studies on erosion has considered the erosion of grains subjected to a unidirectional and homogeneous (translation invariant) tangential flow [14][15][16]. This configuration is relevant for dune formation in the desert [17][18][19][20][21], or for sediment transport in rivers [22][23][24][25]. Although this simple flow configuration allows obtaining relevant scaling laws for sediment erosion and transport, various configurations involve a granular bed subjected to a flow that is not homogeneous.…”