Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow

The transport inception of immersed grains is studied experimentally with laminar flow conditions in a Hele-Shaw cell when varying the tilt angle of the cell and the water flow rate. Varying these two parameters, grains are either motionless, rolling on the bed surface, or avalanching downwards. This paper focuses on the determination of the onset for grain motion either by erosion or by avalanche. For a horizontal interface, onset for erosion corresponds to a constant critical Shields number ${\theta }_c=0.14$ at small particle Reynolds number $({\mathrm{Re}}_d<1)$ but decreases as ${\mathrm{Re}}_d^{-1}$ at larger particle Reynolds number $({\mathrm{Re}}_d>1)$ . For tilted bed, the onset of erosion increases when the flow is opposed to gravity. Both results are compared to a standard model based on a balance of the forces acting on a single grain lying on a tilted plane. When tilt angles are large, avalanches occur. The maximum angle of stability is modified by the flow and increases slightly when the flow acts against gravity. This behavior is compared to a continuous model where a few layers of grains are about to slide.