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

Paul B. Umbanhowar, Harry L. Swinney

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

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 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 languageEnglish (US)
Pages (from-to)344-362
Number of pages19
JournalPhysica A: Statistical Mechanics and its Applications
Volume288
Issue number1-4
DOIs
StatePublished - Dec 15 2000

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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