Nonlinear analysis of the shearing instability in granular gases

Details Nonlinear analysis of the shearing instability in granular gases Nonlinear analysis of the shearing instability in granular gases

2000-02-25

arxiv.org/abs/cond-mat/0002408v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, 4 figure http://www.cecam.fr

Scientific paper

10.1103/PhysRevE.62.3836

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.

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