Wavelength scaling and square/stripe and grain mobility transitions in vertically oscillated granular layers

Laboratory experiments are conducted to examine granular wave patterns near onset as a function of the container oscillation frequency f and amplitude A, layer depth H, and grain diameter D. The primary transition from a flat grain layer to standing waves occurs when the layer remains dilated after making contact with the container. With a flat layer and increasing dimensionless peak container acceleration Γ=4π2f2A/g (g is the acceleration due to gravity), the wave transition occurs for Γ≈2.6, but with decreasing Γ the waves persist to Γ=2.2. For 2.2<Γ<3.8, patterns are squares for ffss; H determines the square/stripe transition frequency . The dispersion relations for layers with varying H collapse onto the curve when the peak container velocity v=2πAf exceeds a critical value, . Local collision pressure measurements suggest that vgm is associated with a transition in the horizontal grain mobility: for v>vgm, there is a hydrodynamic-like horizontal sloshing motion, while for v