Linear stability analysis of rapid granular flow on a slope and density wave formation
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0303543,
title = {Linear stability analysis of rapid granular flow on a slope and density wave formation},
author = {Namiko Mitarai and Hiizu Nakanishi},
journal= {arXiv preprint arXiv:cond-mat/0303543},
year = {2009}
}
Comments
25 pages, 15 figures, submitted to J. Fluid Mech.; larger parameter range investigated, discussions revised