Continuum simulations of shocks and patterns in vertically oscillated granular layers

Abstract

We study interactions between shocks and standing-wave patterns in vertically oscillated layers of granular media using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order. We simulate a layer of grains atop a plate that oscillates sinusoidally in the direction of gravity. Standing waves form stripe patterns when the accelerational amplitude of the plate's oscillation exceeds a critical value. Shocks also form with each collision between the layer and the plate; we show that pressure gradients formed by these shocks cause the flow to reverse direction within the layer. This reversal leads to an oscillatory state of the pattern that is subharmonic with respect to the plate's oscillation. Finally, we study the relationship between shocks and patterns in layers oscillated at various frequencies and show that the pattern wavelength increases monotonically as the shock strength increases.

12 pages, 9 figures

References in corpus (5)

• Patterns and Collective Behavior in Granular Media: Theoretical Concepts
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations
• Fluctuating hydrodynamics for dilute granular gases
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Cited by in corpus (2)

• A numerical study of the Navier-Stokes transport coefficients for 2D granular hydrodynamics
• Time Dependence and Density Inversion in Simulations of Vertically Oscillated Granular Layers