Linear stability analysis of rapid granular flow on a slope and density wave formation

Details Linear stability analysis of rapid granular flow on a slope and density wave formation Linear stability analysis of rapid granular flow on a slope and density wave formation

2003-03-26

arxiv.org/abs/cond-mat/0303543v2

J. Fluid Mech. 507, 309 (2004).

Physics

Condensed Matter

Statistical Mechanics

25 pages, 15 figures, submitted to J. Fluid Mech.; larger parameter range investigated, discussions revised

Scientific paper

10.1017/S002211200400881X

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable against the long-wavelength perturbations longitudinal to the flow direction for certain parameter ranges to form the density wave, in contrast with the finite wavelength instability against the transverse perturbation (Forterre & Pouliquen 2002). It is shown that the instability can be understood as the the long-wave instability of the kinematic waves in a quasi-one dimensional system. The results are compared with our previous molecular dynamics simulations (Mitarai & Nakanishi 2001), where the spontaneous density wave formation has been found.

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