Standing wave patterns in shallow beds of vibrated granular material

Conventional and high-speed video imaging was used to observe surface waves in vertically oscillated, thin layers of dry, noncohesive granular material. The onset of wave formation is pressure dependent and sensitive to the preparation of the particle surface. The dispersion relation of these waves is different at high and low frequencies, and the transition can be explained within the context of a hydrodynamical model by the introduction of a frequency dependent viscous cut-off that dominates at high frequency. High-speed imaging also reveals a qualitative change in individual particle movement at high and low frequencies, and the compressibility of the granular layer.