Laboratory rivers*

Alluvial rivers transport sediment, and build their own bed out of it. The flow entrains superficial grains of sediment and deposit them downstream, thus deforming the channel that confines it. This fluid-structure coupling generates ripples, dunes, bars and meanders through various instabilities. It also selects a river's size and slope.

To entrain a sediment grain, the flow-induced shear stress must overcome its weight. This threshold, typical of granular materials, sets the characteristic size of alluvial rivers. Beyond this threshold, however, a river needs to balance the cross-stream fluxes of sediment to maintain its bed. Unfortunately, these fluxes are barely accessible to field measurements.

Creating small rivers in laboratory experiments is an old idea, but only now can we track thousands of individual grains, as they travel downstream, to reveal the statistics of sediment transport, and their consequences on a river's shape.

In a laminar flume, we find that the roughness of the bed causes the traveling particles to roam across its surface. This random walk induces a Fickian flux which tends to homogenize the transport of sediment. Meanwhile, the bed assumes a convex shape which brings the traveling grains near its center. As a result, the sediment flux distributes itself in this self-organized potential well according to Maxwell-Boltzman statistics.

The same mechanism allows laboratory rivers to adjust their cross-section and their width to the sediment discharge: they widen and shallow to accommodate a larger input. Beyond a critical sediment discharge, however, a river destabilizes into a braid of intertwined channels. We suggest that a new instability, driven by bedload diffusion, might explain this transition.

Finally, we look for the expression of these dynamics in large sedimentary structures deposited by rivers: alluvial fans.