Hydrodynamic singularities and clustering in a freely cooling inelastic gas

Efi Efrati; Eli Livne; Baruch Meerson

doi:10.1103/physrevlett.94.088001

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Hydrodynamic singularities and clustering in a freely cooling inelastic gas

Efi Efrati·Eli Livne·Baruch Meerson

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Abstract

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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Efi Efrati, Eli Livne, Baruch Meerson. 2004-12-03. Hydrodynamic singularities and clustering in a freely cooling inelastic gas. https://doi.org/10.1103/physrevlett.94.088001

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