Stability of uniform shear flow

The stability of idealized computer shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo simulation of this equation is compared with a hydrodynamic description including non-Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for $t<\mathrm{}{50t}_0,$ where $t_0$ is the mean free time. Longer time simulations up to ${2000t}_0$ are used to identify the asymptotic state as a spatially nonuniform quasistationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.