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 and 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 and Nakanishi 2001), where spontaneous density wave formation was found.
| Original language | English |
|---|---|
| Pages (from-to) | 309-334 |
| Number of pages | 26 |
| Journal | Journal of Fluid Mechanics |
| Issue number | 507 |
| DOIs | |
| Publication status | Published - May 25 2004 |
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All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
Cite this
Linear stability analysis of rapid granular flow down a slope and density wave formation. / Mitarai, Namiko; Nakanishi, Hiizu.
In: Journal of Fluid Mechanics, No. 507, 25.05.2004, p. 309-334.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Linear stability analysis of rapid granular flow down a slope and density wave formation
AU - Mitarai, Namiko
AU - Nakanishi, Hiizu
PY - 2004/5/25
Y1 - 2004/5/25
N2 - 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 and 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 and Nakanishi 2001), where spontaneous density wave formation was found.
AB - 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 and 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 and Nakanishi 2001), where spontaneous density wave formation was found.
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U2 - 10.1017/S002211200400881X
DO - 10.1017/S002211200400881X
M3 - Article
SP - 309
EP - 334
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
IS - 507
ER -