Hydrodynamic singularities and clustering in a freely cooling inelastic gas

Efi Efrati*, Eli Livne, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageAmerican English
Article number088001
JournalPhysical Review Letters
Issue number8
StatePublished - 4 Mar 2005


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