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

Namiko Mitarai, Hiizu Nakanishi

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
Pages (from-to)309-334
Number of pages26
JournalJournal of Fluid Mechanics
Issue number507
DOIs
Publication statusPublished - May 25 2004

Fingerprint

Linear stability analysis
slopes
perturbation
Wavelength
hydrodynamic equations
steady flow
Steady flow
planetary waves
wavelengths
Molecular dynamics
Gravitation
Kinematics
kinematics
Hydrodynamics
gravitation
molecular dynamics
Computer simulation
simulation

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 journalArticle

@article{0b74690dc4a948bbb63c02f975da55df,
title = "Linear stability analysis of rapid granular flow down a slope and density wave formation",
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.",
author = "Namiko Mitarai and Hiizu Nakanishi",
year = "2004",
month = "5",
day = "25",
doi = "10.1017/S002211200400881X",
language = "English",
pages = "309--334",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",
number = "507",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=2542580159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2542580159&partnerID=8YFLogxK

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 -