HYDRODYNAMIC MODES OF A GRANULAR SHEAR-FLOW

Linear hydrodynamic modes for a monodisperse granular medium of slightly inelastic spheres in the collisional regime are considered. The dispersion relation is found for a flow in which the grains are fluidized by external shearing, such as occurs in a planar shear cell. One important consequence of this analysis is that flows used in typical shear cells may be supersonic, i.e., that the propagation speed of compressional density waves can be lower than the granular flow speed. Also, even at low frequencies and long wavelengths, there is nontrivial damping of density waves due to the dissipation of fluctuation energy into true thermal energy. This implies that it is important to consider both the strong compressibility and the dissipative processes when considering collective modes of these systems. The implications of this for linear stability are examined for the example of a Couette flow.