hide
Free keywords:
-
Abstract:
Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense
clusters only due to dissipative interactions. Here we show that the evolution of a dilute, freely
cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal
velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of
the granular Navier-Stokes equations show that irrespective of the coefficient of restitution, density
or initial velocity distribution, the density fluctuations follow a universal quadratic dependence
on the system’s Mach number. We find that the clustering exhibits a scale-free dynamics but the
clustered state becomes observable when the Mach number is approximately of O(1). Our results
provide a method to determine the age of a granular gas and predict the macroscopic appearance
of clusters.
