Subcritical and supercritical granular flow around an obstacle on a rough inclined plane

Abstract

A blunt obstacle in the path of a rapid granular avalanche generates a bow shock (a jump in the avalanche thickness and velocity), a region of static grains upstream of the obstacle, and a grain-free region downstream. Here, it is shown that this interaction is qualitatively altered if the incline on which the avalanche is flowing is changed from smooth to rough. On a rough incline, the friction between the grains and the incline depends on the flow thickness and speed, which allows both rapid (supercritical) and slow (subcritical) steady uniform avalanches. For supercritical experimental flows, the material is diverted around a blunt obstacle by the formation of a bow shock and a static dead zone upstream of the obstacle. Downslope, a grain-free vacuum region forms, but, in contrast to flows on smooth beds, static levees form at the boundary between the vacuum region and the flow. In slower, subcritical, flows the flow is diverted smoothly around the dead zone and the obstacle without forming a bow shock. After the avalanche stops, signatures of the dead zone, levees and (in subcritical flows) a deeper region upslope of the obstacle are frozen into the deposit. To capture this behaviour, numerical simulations are performed with a depth-averaged avalanche model that includes frictional hysteresis and depth-averaged viscous terms, which are needed to accurately model the flowing and deposited regions. These results may be directly relevant to geophysical mass flows and snow avalanches, which flow over rough terrain and may impact barriers or other infrastructure.