Long surface wave instability in dense granular flows

TL;DR

This study experimentally investigates long surface wave instability in dense granular flows on inclined planes, comparing results with linear stability theory and revealing both predictive successes and limitations related to granular rheology.

Contribution

It provides a detailed experimental analysis of wave instability thresholds and dispersion relations, and evaluates the accuracy of Saint-Venant equations with a specific friction law for granular flows.

Findings

Theory predicts stability threshold and phase velocity accurately.

Theory fails to predict the cutoff frequency of the instability.

Granular rheology significantly influences the instability characteristics.

Abstract

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely measured by imposing a controlled perturbation at the entrance of the flow and measuring its evolution along the slope. The results are compared with the prediction of a linear stability analysis conducted in the framework of the depth-averaged or Saint-Venant equations. We show that when the friction law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations, the theory is able to predict quantitatively the stability threshold and the phase velocity of the waves but fails in predicting the observed cutoff frequency. The instability is shown to be of the same nature as the long wave instability observed in classical fluids but with characteristics that can dramatically differ due to the specificity of the granular rheology.