Dynamics of Freely Cooling Granular Gases

TL;DR

This study investigates the long-term behavior of freely cooling granular gases in two dimensions, revealing algebraic energy decay, universal velocity distributions, and coherent particle motion in the clustering regime through large-scale simulations.

Contribution

It provides new insights into the late-time dynamics and velocity statistics of granular gases, highlighting universal behaviors and potential Burgers-like descriptions.

Findings

Kinetic energy decays as t^{-1} in dilute systems.

Velocity distribution becomes Gaussian at late times.

Particles move coherently with small local velocity fluctuations.

Abstract

We study dynamics of freely cooling granular gases in two-dimensions using large-scale molecular dynamics simulations. We find that for dilute systems the typical kinetic energy decays algebraically with time, E(t) ~ t^{-1}, in the long time limit. Asymptotically, velocity statistics are characterized by a universal Gaussian distribution, in contrast with the exponential high-energy tails characterizing the early homogeneous regime. We show that in the late clustering regime particles move coherently as typical local velocity fluctuations, Delta v, are small compared with the typical velocity, Delta v/v ~ t^{-1/4}. Furthermore, locally averaged shear modes dominate over acoustic modes. The small thermal velocity fluctuations suggest that the system can be heuristically described by Burgers-like equations.