Surface Instability of a Vertically Oscillating Granular Layer

In the study of the surface instability of a vertically oscillating granular layer, we obtained experimentally the phase diagram for the surface states of the layer in the driving frequency-acceleration plane, and measured the dispersion relation for the surface waves in a granular layer in comparison to that in viscous fluids. Our experiments show that the onset dimensionless acceleration increases with the driving frequency, and the wavelength of the surface waves increases with the depth of granular layer. These experimental results are in agreement with our theoretical model qualitatively.