Continuum simulations of shocks and patterns in vertically oscillated granular layers

TL;DR

This study uses continuum simulations to analyze how shocks influence pattern formation in vertically oscillated granular layers, revealing the relationship between shock strength and pattern wavelength.

Contribution

It introduces a detailed continuum model simulation of shock and pattern interactions in granular layers, highlighting the role of shocks in pattern oscillations and wavelength variation.

Findings

Shocks cause flow reversal within the granular layer.

Pattern wavelength increases with shock strength.

Oscillatory patterns are subharmonic to the oscillation frequency.

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.