Sediment load determines the shape of rivers.

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.

Diffusive evolution of experimental braided rivers.

Water flowing over a loose granular bed organizes into a braided river, a network of ephemeral and interacting channels. The temporal and spatial evolution of this network of braided channels is not yet quantitatively understood. In ∼ 1 m-scale experiments, we found that individual channels exhibit a self-similar geometry and near-threshold transport conditions. Measurements of the rate of growth of topographic correlation length scales, the time scale of system-slope establishment, and the random spatial decorrelation of channel locations indicate together that the evolution of the braided river system may be diffusive in nature. This diffusion is due to the separation of scales between channel formation and network evolution, and the random motion of interacting channels when viewed at a coarse-grained scale.