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arXiv · 1510.06644

A universal scaling law for the evolution of granular gases

Mathias Hummel·James P. D. Clewett·Marco G. Mazza
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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 $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.

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Mathias Hummel, James P. D. Clewett, Marco G. Mazza. 2015-10-21. A universal scaling law for the evolution of granular gases. https://doi.org/10.1209/0295-5075%2F114%2F10002

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