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

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 dimensi onless peak container acceleration Gamma = 4 pi (2)f(2)A/g (g is the accele ration due to gravity), the wave transition occurs for Gamma approximate to 2.6, but with decreasing Gamma the waves persist to Gamma = 2.2. For 2.2 < <Gamma> < 3.8, patterns are squares for f < f(ss) and stripes for f > f(ss ); H determines the square/stripe transition frequency f(ss) = 0.33 rootg/H . The dispersion relations for layers with varying H collapse onto the curv e lambda /H = 1.0 + 1.1(f rootH/g)(-1.32+/-0.03) when the peak container ve locity v = 2 pi Af exceeds a critical value, v(gm) approximate to 3 root Dg . Local collision pressure measurements suggest that v(gm) is associated wi th a transition in the horizontal Brain mobility: for v > v(gm), there is a hydrodynamic-like horizontal sloshing motion, while for v < v(gm), the gra ins are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at v(gm) less than f(ss) and v < v(g m), patterns are tenuous and disordered. (C) 2000 Elsevier Science B.V. All rights reserved.