Granular-solid-gas Transition, Non-locality, and Coulomb Friction Law: The Curious Case of Sediment Transport.

Today it is well established that a macroscopic Coulomb friction (yield) criterion controls the transition between quasistatic or creeping granular flows and liquid-like granular flows: when the dynamic friction coefficient $\mu$ (i.e., the ratio between the tangential and normal granular stress) exceeds a critical value, the granular medium flows like a liquid. This liquid-like regime can be described by a rheology relating $\mu$ to a single local flow property, such as the particle volume fraction, except near the transition, where non-local effects may emerge. Here we find from numerical particle-scale simulations that a prominent class of geophysical granular flows -- non-suspended sediment transport mediated by the turbulent shearing flow of a Newtonian fluid over an erodible granular bed -- can strongly disobey these classical behaviors, which is accentuated by a non-local rheology even relatively far from the flow threshold. The reason is a transition (except for relatively intense transport conditions) from the quasistatic bed to a gas-like transport layer through a very thin transient creeping-like zone around the bed surface: a liquid-like regime does not necessarily exist. Nevertheless, we find that $\mu$ is a universal approximate constant at an appropriately defined bed-transport-layer interface, which is usually located within the gas-like region of the granular flow. We show that this apparent Coulomb friction law is a signature of a steady transport state in which transported particles continuously rebound at the bed surface. The only exception is very viscous bedload transport, for which it follows from the liquid-like rheology of dense viscous suspensions. Our results provide the theoretical base for understanding the scaling of the rate and threshold of non-suspended sediment transport, which are two central problems in Earth and planetary geomorphology.