Long-surface-wave instability in dense granular flows

By Yoël Forterre, Olivier Pouliquen. Journal of Fluid Mechanics, 2003

138 citations recorded by the source corpus.

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 down 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.

Subfields: Computational Mechanics, Management, Monitoring, Policy and Law, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/02a5b99d800909fcb3680cb4c3ef60f0caf85856

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Citations in the corpus

Flows of Dense Granular Media (2008, background): “…proposed more complex basal friction laws μb (〈u〉, h) that lead to quantitative predictions in complex situations such as a propagating steady front, mass spreading, or surface instabilities (Forterre & Pouliquen 2003, Mangeney-Castelnau et al. 2007, Pouliquen 1999a, Pouliquen & Forterre 2002).”
Patterns and collective behavior in granular media: Theoretical concepts (2005, background): “…instabilities in 7 relatively small-scale flows, such as flow past obstacle (Rericha et al., 2002), convection (Livne et al., 2002a,b), floating clusters (Meerson et al., 2003), longitudinal rolls (Forterre and Pouliquen, 2002, 2003), patterns in vibrated layers (Bougie et al., 2005) and others.”