2000/01/27 by Paul B. Umbanhowar, Harry L. Swinney · 46 citations
Chemistry · Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Acceleration #Aeolian processes and effects #Amplitude #Chemistry #Classical mechanics #Composite material #Container (type theory) #Dimensionless quantity #Dispersion (optics) #Geology and Paleoclimatology Research #Geometry #Granular flow and fluidized beds #Materials science #Mechanics #Optics #Optoelectronics #Oscillation (cell signaling) #Physics #Slosh dynamics #Square (algebra) #Wavelength #nlin.AO #nlin.PS
paper · pdf · doi:10.1016/s0378-4371(00)00432-5
published in Physica A Statistical Mechanics and its Applications 288(1-4), 344-362 (Elsevier BV) · 21 pages, 15 figures, submitted to Physica A
arxiv created 2000/01/27 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 G = 4 pi2 f2 A/g (g is the acceleration due to gravity), the wave transition occurs for G=2.6, but with decreasing G the waves persist to G=2.2. For 2.2<G<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)0.5. The dispersion relations for layers with varying H collapse onto the curve L/H=1.0+1.1[f(H/g)0.5]^(-1.32 +/- 0.03) (L is the wavelength) when the peak container velocity v exceeds a critical value vgm of approximately 3 (Dg)0.5. 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.