Long-time tails in freely cooling granular gases

TL;DR

This paper investigates the long-time decay behavior of auto-correlation functions in freely cooling granular gases, revealing distinct power-law and exponential decay patterns for different physical quantities.

Contribution

It provides the first detailed analysis of long-time tails in velocity, shear stress, and heat flux correlations in granular gases, supported by numerical simulations.

Findings

Velocity and shear stress correlations decay as τ^{-d/2}.

Heat flux correlation decays as τ^{-(d+2)/2} exp(-ζ* τ).

Numerical results agree with theoretical predictions.

Abstract

The long-time behavior of the current auto-correlation functions for the velocity, the shear stress and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying $\tau^{-d/2}$, while the correlation function of heat flux decays as $\tau^{-(d+2)/2} \exp(-\zeta^* \tau)$ with the dimensionless cooling rate $\zeta^*$, the spatial dimension $d$ and the scaled time $\tau$ in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.