Hydrodynamic singularities and clustering in a freely cooling inelastic gas.
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.
Efrati
Efi
E
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Livne
Eli
E
Meerson
Baruch
B