Velocity profile of granular flows down a heap described by dimensional analysis

Gravity-driven thick granular flows are relevant to many industrial and geophysical processes. In particular, it is important to know and understand the particle velocity distributions as we get deeper into the flow from the free surface. In this paper, we use dimensional analysis as a tool to reproduce the velocity profile experimentally reported for granular flows down a confined heap for the so-called flowing layer and the creep layer underneath: the grains velocity first decrease linearly from the free surface, and then exponentially.