Shock Instability and Pattern Formation in Vertically Oscillated Granular Media

A layer of grains atop a plate subject to vertical shaking will leave the plate at some time during the oscillation cycle provided that the accelerational amplitude of the plate’s oscillation is greater than the acceleration of gravity. With each subsequent contact of the grains with the plate, shocks form and propagate through the granular layer. Additionally, when the dimensionless accelerational amplitude Γ exceeds a critical value Γ_crit, standing-wave patterns form in the layer, oscillating subharmonically with respect to the oscillation of the plate. We explore the relationship between these shocks and patterns by modeling granular flow using numerical simulations of continuum equations to Navier-Stokes order. These simulations provide a basis to characterize the shocks in these layers and to analyze pattern development in connection with an instability in the shock front as it propagates through the layer.