Surface waves in vertically vibrated granular materials

Noncohesive granular materials driven by a vertically vibrated horizontal surface become unstable when the acceleration exceeds g. Then there is internal convective transport of materials balanced by continuous surface avalanches leading to an inclined surface. We describe studies above the onset to flow where new surface wave motions occur. The surface waves travel upward against gravity on the free surface. They occur only above minimum accelerations and dimensionless energies, and only with large vibration amplitude.