Oscillatory instability in a driven granular gas

– We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite " thermal " walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular hydrodynamics, occurs when the inelasticity of particle collisions exceeds a critical value. Molecular dynamic simulations support the theory and show a stripe-shaped cluster moving back and forth in the middle of the box away from the driving walls. The oscillations are irregular but have a single dominating frequency that is close to the frequency at the instability onset, predicted from hydrodynamics. Introduction. – Granular gas-a system of inelastically colliding hard spheres-is a minimalistic model of granular flow that has received much recent attention [1]. In particular , this model captures clustering, a generic and fascinating phenomenon in rapid granu-lar flows resulting from the collisional loss of the kinetic energy of random motion of particles. The formation and structure of granular clusters have been investigated in many works, both in the context of a freely " cooling " granular gas [2] and for driven granular The basic physics of clustering can often be described in a hydrodynamic language, in terms of a collective condensation mode driven by bulk losses of energy. Similar condensation processes, driven by radiative energy losses in gases and plasmas, have been known for a long time [19]. A complete understanding of the properties of granular gas (a system intrinsically far from equilibrium) is still lacking. One important open question is the exact criteria for the validity of kinetic theory and Navier-Stokes hydrodynamics, developed in the 80-ies [20, 21]. Driven granular gas has the advantage that a steady state is achievable: the energy supplied into the system can be balanced by the collisional energy losses. We have focused in this work on a simple model: inelastic smooth hard spheres confined in a rectangular box and driven by two opposite " thermal " walls at zero gravity. Prototypical granular systems of this type were considered by many workers. In the early work, theoretical [5,8,10] and experimental [4], the " stripe state " : a denser and " colder " stripe-like cluster of particles, away from the driving wall(s), was documented. The formation of the stripe state has a simple explanation. Due to the inelastic particle collisions, the granular temperature goes down with an increase of the distance from the thermal wall(s). …