Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas

TL;DR

This study uses particle simulations to analyze how translational and rotational velocities in a dilute granular gas under shear flow are correlated, revealing Gaussian distributions near smooth and rough limits and non-Gaussian tails elsewhere.

Contribution

It demonstrates the correlation between translational and rotational velocities and characterizes the velocity distribution functions across different collision regimes.

Findings

Velocities are strongly correlated in direction.

Distributions are Gaussian near smooth and rough limits.

Non-Gaussian tails follow stretched exponential forms.

Abstract

Using particle simulations of the uniform shear flow of a rough dilute granular gas, we show that the translational and rotational velocities are strongly correlated in direction, but there is no orientational correlation-induced singularity at perfectly smooth ($\beta=-1$) and rough ($\beta=1$) limits for elastic collisions ($e=1$); both the translational and rotational velocity distribution functions remain close to a Gaussian for these two limiting cases. Away from these two limits, the orientational as well as spatial velocity correlations are responsible for the emergence of non-Gaussian high velocity tails. The tails of both distribution functions follow stretched exponentials, with the exponents depending on normal ($e$) and tangential ($\beta$) restitution coefficients.