Rapid granular flows down inclined planar chutes. Part 2. Linear stability analysis of steady flow solutions

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Abstract

The linear stability of steady solutions for a rapid granular flow down an inclined chute, modelled using a kinetic theory continuum model, is analysed. The previous studies of Forterre & Pouliquen (J. Fluid Mech., vol. 467, 2002, p. 361) and Mitarai & Nakanishi (J. Fluid Mech., vol. 507, 2004, p. 309) are extended by considering fully three-dimensional perturbations, allowing variations in both the cross-slope and downslope directions, as well as normal to the base. Our results demonstrate the existence of three qualitatively different unstable perturbations, each of which can be the most rapidly growing instability for different steady flows. By considering the linear stability of many steady solutions along macroscopic flow curves, we show that linear stability occurs in only a small part of parameter space, and furthermore the regions of linear instability do not correlate with density inversion of the underlying steady solutions. Our results suggest that inelastic clustering is the dominant instability mechanism.
Translated title of the contributionRapid granular flows down inclined planar chutes. Part 2. Linear stability analysis of steady flow solutions
Original languageEnglish
Pages (from-to)461 - 488
Number of pages28
JournalJournal of Fluid Mechanics
Volume652
Early online date19 May 2010
DOIs
Publication statusPublished - Jun 2010

Bibliographical note

Publisher: Cambridge University Press

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