On the stability of rapid granular flows

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Abstract
Numerical simulations of rapid granular flows in large periodic domains have demonstrated the existence of an ‘inelastic microstructure’ characterized by agglomerations of particles into clusters. In the present work the phenomenon of particle clustering is considered to be a manifestation of hydrodynamic instability of the equations governing the dynamics of rapid granular flows. A linear stability analysis of the simple shear flow of smooth, slightly, inelastic disks and spheres is carried out utilizing the governing equations formulated by the kinetic theory. The results indicate that disturbances of large wavelengths initially grow at an exponential rate for any value of the restitution coefficient. The results also demonstrate that this phenomenon will not be exposed in numerical simulations within small periodic domains, because the range of possible disturbance wavelengths is limited by the size of the periodic domain.