Hydrodynamic singularities and clustering in a freely cooling inelastic gas

Details Hydrodynamic singularities and clustering in a freely cooling inelastic gas Hydrodynamic singularities and clustering in a freely cooling inelastic gas

2004-12-03

arxiv.org/abs/cond-mat/0412081v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.94.088001

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.

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