Roll-waves prediction in dense granular flows

This paper analyses conditions for roll-waves formation in homogeneous granular flows with the aim of predicting their occurrence in finite length channels. With reference to a wide class of constitutive equations of the flowing medium, the response of the linearized one-dimensional flow model to a pointwise instantaneous disturbance is studied and a closed form of the Green’s function, in both stable and unstable conditions, is provided. The exponential growth of the disturbance peak is used to predict the spatial evolution of roll-waves in dry flows of dense granular materials and a criterion for the minimum channel length necessary to appreciate roll-wave development is proposed. The comparison among theoretical and experimental data available in the literature appears promising.