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

Published online by Cambridge University Press:  12 May 2004

NAMIKO MITARAI  and
HIIZU NAKANISHI
NAMIKO MITARAI
Affiliation:
Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan
HIIZU NAKANISHI
Affiliation:
Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan
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Abstract

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

Type
Papers
Information
Journal of Fluid Mechanics , Volume 507 , 25 May 2004 , pp. 309 - 334
Copyright
© 2004 Cambridge University Press

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