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.

了解河流如何适应其携带的沉积物负荷对于预测景观的演变至关重要。然而，目前还没有基于物理的模型能够可靠地捕捉河流基本特性（例如其形状或坡度）对沉积物排放的依赖性，即使是在实验室河流的简单情况下也是如此。在这里，我们展示了作用在沉积物颗粒上的流体应力和重力之间的平衡，以及沉积物的跨流扩散，如何决定携带沉积物作为床质的层流实验室河流的形状和沉积物通量剖面。使用这个无需任何调整就能可靠地重现实验的模型，我们证实了最初由 Parker [G. 帕克，J.流体机械。89, 127–146 (1978)]，河流被限制存在于泥沙运动阈值附近（约 20% 以内）。该限制是由流体-沉积物相互作用设定的，与河流携带的水和沉积物负荷无关。因此，随着输沙总量的增加，河流的输沙通量强度（单位宽度的输沙量）达到饱和，只有加宽河流才能输送更多的泥沙。在这种大流量状态下，水流中动量的跨流扩散允许沉积物运输。相反，在弱输送状态下，输送的沉积物集中在河流中心周围，而不会显着改变河流形状。如果这一理论适用于天然河流，那么河流的纵横比可能成为泥沙排放量的代表——众所周知，泥沙排放量很难在现场测量。