The morphology of alluvial rivers

Alluvial rivers form their channel in the material they transport, producing a varied collection of bed shapes, from deep single-thread channels to wide and shallow braids. Laboratory flumes produce similar morphologies at the centimeter scale, while braided rivers can spread over a few kilometers, suggesting that the same basic phenomena express themselves across scales. We conjecture that the competition between gravity and diffusion, at the scale of a sediment grain, controls the morphology of alluvial rivers. The classical threshold theory, which neglects diffusion, explains the relationship between river width and discharge [1]. However, it is valid only when bedload transport vanishes. When the river transports sediments, gravity pulls the grains towards the center of the channel, precluding equilibrium within this theoretical framework [2]. Based on laboratory experiments, we suggest that each bedload grain follows a random walk in the transverse direction. Consequently, sediments diffuse towards the less active areas of the bed, thus counteracting gravity by continuously rebuilding the river's bank. As the sediment discharge increases, this balance requires a wider and narrower channel, until the river becomes unstable. [1] R.E. Glover and Q.L. Florey, Stable channel profiles, US Bur. Reclamation, Hydr., 325, 1951. [2] G. Parker, Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river, J. Fluid Mech., 89, 1, 1978.