Shear state of freely evolving granular gases

TL;DR

This paper uses hydrodynamic equations to predict and verify the formation of a steady shear band state in a freely evolving granular gas, showing small density fluctuations and a scaled velocity field, with good agreement between theory and simulations.

Contribution

It introduces a hydrodynamic theory predicting a shear band state in granular gases and validates it with numerical simulations for low inelasticity.

Findings

Formation of a two-band shear state with steady density profile

Small density fluctuations without clustering

Velocity field scaling with the square root of temperature

Abstract

Hydrodynamic equations are used to identify the final state reached by a freely evolving granular gas above but close to its shear instability. The theory predicts the formation of a two bands shear state with a steady density profile. There is a modulation between temperature and density profiles as a consequence of the energy balance, the density fluctuations remaining small, without producing clustering. Moreover, the time dependence of the velocity field can be scaled out with the squared root of the average temperature of the system. The latter follows the Haff law, but with an effective cooling rate that is smaller than that of the free homogeneous state. The theoretical predictions are compared with numerical results for inelastic hard disks obtained by using the direct Monte Carlo simulation method, and a good agreement is obtained for low inelasticity.