Scale-free channeling patterns near the onset of erosion of sheared granular beds

Abstract

Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we study experimentally the collective dynamics of the moving particles, using a set-up where the system spontaneously evolves toward the erosion onset. We find that the spatial organization of the erosion flux is heterogeneous in space, and occurs along channels of local flux $σ$ whose distribution displays scaling near threshold and follows $P(σ)\sim J/σ$, where $J$ is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction. We show that these results quantitatively agree with a model where the dynamics is governed by the competition of disorder (which channels mobile particles) and particle interactions (which reduces channeling). These observations support that for laminar flows, erosion is a dynamical phase transition which shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.

8 pages, 6 figures