Streamwise streaks induced by bedload diffusion

Abstract

A fluid flowing over a granular bed can move its superficial grains, and eventually deform it by erosion and deposition. This coupling generates a beautiful variety of patterns, such as ripples, bars and streamwise streaks. Here, we investigate the latter, sometimes called ‘sand ridges’ or ‘sand ribbons’. We perturb a sediment bed with sinusoidal streaks, the crests of which are aligned with the flow. We find that, when their wavelength is much larger than the flow depth, bedload diffusion brings mobile grains from troughs, where they are more numerous, to crests. Surprisingly, gravity can only counter this destabilising mechanism when sediment transport is intense enough. Relaxing the long-wavelength approximation, we find that the cross-stream diffusion of momentum mitigates the influence of the bed perturbation on the flow, and even reverses it for short wavelengths. Viscosity thus opposes the diffusion of entrained grains to select the most unstable wavelength. This instability might turn single-thread alluvial rivers into braided channels.