Formation and evolution of density singularities in hydrodynamics of inelastic gases.
We use hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a finite-time density blowup, where the gas pressure remains finite. The density blowup signals the formation of close-packed clusters. The blowup dynamics is universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass pointlike singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel.
Itzhak
I
Fouxon
Baruch
B
Meerson
Michael
M
Assaf
Eli
E
Livne