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

Namiko Mitarai·Hiizu Nakanishi
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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.

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BibTeXRIS

Namiko Mitarai, Hiizu Nakanishi. 2003-09-15. Linear stability analysis of rapid granular flow on a slope and density wave formation. https://doi.org/10.1017/s002211200400881x

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