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 f<fss and stripes for f>fss; H determines the square/stripe transition frequency fss = 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 = 2πAf exceeds a critical value, vgm≈3D̄ḡ. 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<vgm, the grains are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at vgm less than fss and v<vgm, patterns are tenuous and disordered.
|Original language||English (US)|
|Number of pages||19|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - Dec 15 2000|
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics