The onset of instabilities in discretely shaken granular layers

Abstract

A simple computational model is introduced to study a system consisting of a discretely shaken granular layer. Despite the simplicity the model shows the formation of instabilities in the layer and the later development of granular heaplets. We show analytically that the onset of instabilities is dependent on the density or thickness of the layer and this result is justified by the subsequent computer simulations. Our simulations also show that the development of heaplets can be divided into three stages: an early stationary stage, an intermediate growing stage and a late-time saturated stage. In the early stage, the average volume of the heaplets remains almost unchanged until the system crosses over to the intermediate growing stage. The average length of time that the system remains in the early stage defines the average onset time of the instabilities, k ₀ and this depends on the shaking intensity, γ. The onset time k ₀ seems to diverge for values of γ>γ_c where γ^c≃14. In the growing stage, the average volume of the heaplets grows with time and can be approximated by a power law with a growth exponent, z which depends on γ and from our simulation z depends linearly on γ. The late-time saturated stage is where most of the particles are trapped in a big heap and this big heap is in equilibrium with the surrounding granular gas.