Spontaneous development of 3-D structure in sheared granular flows

Original · EN

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, vₓ=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 vₓ=ay+sin(2πz/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.