Dilatancy, buckling, and undulations on a vertically vibrating granular layer.

We report experiments on a vertically vibrated quasi-two-dimensional granular layer of lead spheres showing subharmonic undulations and ripples, which are associated with horizontal dilatation at the impingement of the bottom wall. By systematically changing frequency and amplitude of external forcing, as well as the container sizes and layer height, we observed various eigenmodes of undulations, whose selection is determined by the amount of configuration changes in densely packed particles along the bottom wall. Resulting enhancement of horizontal stress induces the buckling and bending of the granular layer of successively higher modes.