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

• Published in: Physica A 2000-12, Vol.288 (1), p.344-362
• Main Authors: Umbanhowar, Paul B., Swinney, Harry L.
• Format: Article
• Language: English
• Subjects: Bifurcation; Granular media; Pattern; Wavelength
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(00)00432-5

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=4 π 2f 2A/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 f ss ; H determines the square/stripe transition frequency f ss=0.33 g/H . The dispersion relations for layers with varying H collapse onto the curve λ/H=1.0+1.1(f H/g ) −1.32±0.03 when the peak container velocity v=2π Af exceeds a critical value, v gm≈3 Dg . Local collision pressure measurements suggest that v gm is associated with a transition in the horizontal grain mobility: for v>v gm , there is a hydrodynamic-like horizontal sloshing motion, while for v