Patterns in 3D Vertically Oscillated Granular Layers: Simulation and Experiment

Abstract

Numerical simulations and laboratory experiments are conducted for thin layers of particles in a vertically oscillated container as a function of the frequency $f$, amplitude $A$, and depth $H$. The same standing wave patterns (stripes, squares, or hexagons oscillating at $f/2$ or $f/4$) and wavelengths are obtained in the simulations and experiments for a wide range of $(f,A)$ and two layer depths. Two model parameters are determined by fits at just two points $(f,A,H)$. Simulation results lead to heuristic arguments for the onset of patterns and the crossover from squares to stripes.