Long-surface-wave instability in dense granular flows

• Published in: Journal of fluid mechanics Vol. 486; pp. 21 - 50
• Main Authors: FORTERRE, YOËL, POULIQUEN, OLIVIER
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2003; Cambridge University Press (CUP)
• Subjects: Cross-disciplinary physics: materials science; rheology; Engineering Sciences; Exact sciences and technology; Fluid mechanics; Granular materials; Granular solids; Material form; Physics; Rheology; Stability analysis; Rough wall; Test facilities; Surface waves; Sand; Inclined plan; Glass; Granular flow; Linear stability; Experimental study
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112003004555

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.