Instability in a Sand Heap

When a bead heap is submitted to low-frequency (ω2π=10-1000 Hz) vertical vibrations at a large enough amplitude a, its horizontal free surface becomes unstable and a stationary state is reached. This one is characterized firstly by a free surface which is inclined within an angle θ to the horizontal, secondly by a continuous flow of particles rolling down the free surface, and thirdly by a convective transport inside the material which refills the top of the heap with new beads. We demonstrate that a control parameter is the vibration acceleration γ=aω².