Equilibrium morphology of laminar rivers

The flow of a viscous fluid over a bed of plastic sediment spontaneously generates single-thread channels. With time, these analogues of alluvial rivers reach a reproducible steady state, exhibiting a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combination of gravity and flow-induced stress maintains the bed surface at the threshold of motion.\footnote{Seizilles et al., \textbf{Phy. Rev. E.} 87, 052204} If the river transports sediments, gravity pulls the moving grains towards the center of the channel.\footnote{Parker \textbf{J. Fluid Mech.} 89, 127-146} Because of bed roughness, these moving grains follow a random walk in the transverse direction.\footnote{Seizilles et al., \textbf{Phys. Fluids} 26, 013302} Consequently, sediments diffuse towards the less active areas of the bed, thus counteracting gravity by continuously rebuilding the river banks. As the sediment discharge increases, this balance requires a wider and narrower channel, until the river becomes unstable. Based on these experimental observation, we propose a theory explaining how the channel selects its size and slope for given flow and sediment discharges.