Energy Decay in Three-Dimensional Freely Cooling Granular Gas

Abstract

The kinetic energy of a freely cooling granular gas decreases as a power law ${t}^{\ensuremath{-}\ensuremath{\theta}}$ at large times $t$. Two theoretical conjectures exist for the exponent $\ensuremath{\theta}$. One based on ballistic aggregation of compact spherical aggregates predicts $\ensuremath{\theta}=2d/(d+2)$ in $d$ dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts $\ensuremath{\theta}=d/2$ when $2\ensuremath{\le}d\ensuremath{\le}4$. We do extensive simulations in three dimensions to find that while $\ensuremath{\theta}$ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.