A universal scaling law for the evolution of granular gases
Abstract
Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. 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 . Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.
Keywords
Cite
@article{arxiv.1510.06644,
title = {A universal scaling law for the evolution of granular gases},
author = {Mathias Hummel and James P. D. Clewett and Marco G. Mazza},
journal= {arXiv preprint arXiv:1510.06644},
year = {2016}
}