Séminaire régulier IUSTI – 9 févr. 2018 – 11h salle 250

Forme et stabilité des rivières alluviales

Éric Lajeunesse – IPGP, Paris

Alluvial rivers build their bed with the sediment they carry. They obey Lacey’s law which states that the width of a river scales with the square root of its discharge. This universal behavior suggests a common physical origin, but there is no consensus yet about what mechanism selects the size and shape of an alluvial river. Here we produce a small river in a laboratory experiment by pouring a viscous fluid on a layer of plastic sediment (Figure 1). With time, this laminar river reaches a steady-state geometry. In the absence of sediment transport, the combination of gravity and flow-induced stress maintains the bed surface at the threshold of motion. If we impose a sediment discharge, the river adjusts by widening its channel. Particle tracking then reveals that the grains entrained by the flow behave as a collection of random walkers. Accordingly, they diffuse towards the less active areas of the bed. The shape of the river’s cross-section results from the balance between this diffusive flux, which pushes the entrained grains towards the banks, and gravity, which returns them towards the center of the channel. As the sediment discharge increases, the channel gets wider and shallower. Eventually, it destabilizes into new channels. A linear stability analysis suggests that the diffusion of the sediment causes this instability, which could explain the formation of braided rivers.