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

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  • Umbanhowar, Paul B.
  • Swinney, Harry L.

Abstract

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 fss=0.33g/H. The dispersion relations for layers with varying H collapse onto the curve λ/H=1.0+1.1(fH/g)−1.32±0.03 when the peak container velocity v=2πAf exceeds a critical value, vgm≈3Dg. 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

Suggested Citation

  • Umbanhowar, Paul B. & Swinney, Harry L., 2000. "Wavelength scaling and square/stripe and grain mobility transitions in vertically oscillated granular layers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 288(1), pages 344-362.
    • Handle: RePEc:eee:phsmap:v:288:y:2000:i:1:p:344-362
    DOI: 10.1016/S0378-4371(00)00432-5
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