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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2000

Nonlinear analysis of the shearing instability in granular gases

Résumé

It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term is added to the energy equation which accounts for the energy dissipation at collisions and the phenomenological Fourier law is generalized according to previous results. Second, a rescaled time formalism is introduced that maps the homogeneous cooling state into a nonequilibrium steady state. A nonlinear stability analysis of the resulting equations is done which predicts the appearance of flow patterns. A stable modulation of density and temperature is produced that does not lead to clustering. Also a global decrease of the temperature is obtained, giving rise to a decrease of the collision frequency and dissipation rate. Good agreement with molecular dynamics simulations of inelastic hard disks is found for low dissipation.

Dates et versions

hal-00119506 , version 1 (10-12-2006)

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Rodrigo Soto, Michel Mareschal, M. Malek Mansour. Nonlinear analysis of the shearing instability in granular gases. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2000, 62, pp.3836-3842. ⟨hal-00119506⟩
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