Dynamic compressibility of dense granular shear flows

We provide evidence that an assembly of hard non-deformable particles can behave as a compressible medium when slowly sheared. By means of discrete element simulations of frictional discs, we show the existence of transverse and sagittal waves. These waves are associated to a dynamic compressibility which originates from the fact that the average density of such a system effectively depends on the confining pressure. Analysing velocity fluctuations, we show the existence of spontaneous oscillations, whose frequency coincides with that observed at the resonance of forced oscillations. The results are independent of the contact stiffness and the restitution coefficient. They are well reproduced by a continuum model based on a local constitutive relation.