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

Significance The response of erodible granular beds to shearing flows controls numerous natural phenomena. A central aspect is the existence of a threshold stress below which erosion stops, and whose microscopic underpinning is debated. We use an experiment where this threshold is spontaneously reached to study the spatial organization of the erosion flux. We find that erosion is heterogeneous in space and occurs along favored channels whose distribution is extremely broad, with strongly anisotropic spatial correlations. These findings can be quantitatively explained by a model incorporating both the disorder of the static bed and the interactions between mobile particles, establishing a link between erosion and dynamical phase transitions known to occur in disordered environments. 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 setup 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)≈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 that 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.