Depth-integrated equations for entraining granular flows in narrow channels

Flowing over erodible beds, channelized granular avalanches can alter their volume by entraining or detraining basal grains. In detail, entrainment results from a gradual adjustment of stress and velocity profiles over depth, bringing bed material past yield (and vice versa for detrainment). To capture this process, we propose new depth-integrated equations that balance kinetic energy in addition to mass and momentum. The equations require a local granular rheology, assumed viscoplastic, but no extra erosion law. Entrainment rates are instead deduced from the depth-integrated layer dynamics. To check the approach, we obtain solutions for non-equilibrium heap flows, and compare them with experiments conducted in a seesaw channel.