Spontaneous development of 3-D structure in sheared granular flows

TL;DR

This paper uses computer simulations to reveal a three-dimensional instability in sheared granular flows, showing how velocity profiles develop complex structures beyond simple shear, with analytical and numerical agreement.

Contribution

It demonstrates the spontaneous emergence of 3D structures in sheared granular fluids through simulations and linear stability analysis, highlighting a new instability mechanism.

Findings

Identification of a 3D instability in granular flows

Analytical expression for the critical wavevector

Instability persists at low densities

Abstract

Computer simulations of sheared granular fluids, modeled as inelastic hard spheres, are presented which show signs of a uniquely three-dimensional instabilty. In the stable regime, a linear velocity profile, $v_{x}=ay$, with shear rate $a$ is established using Lees-Edwards boundary conditions. In the unstable regime, the velocity profile aquires a dependence on the third dimension of the form $v_{x}=ay+sin(2\pi z/L)$ in a cubic box with sides of length $L$. An analysis of the linearized Navier-Stokes equations shows the presence of an instability and gives a simple expression for the critical wavevector which is quantitatively consistent with the results of simulations and which indicates that the instability persists at low densities.