On the development of inhomogeneities in freely evolving granular gases: The shear state and beyond
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The understanding of the mechanisms leading to the formation of inhomogeneities in freely evolving granular gases is important to establish, for instance, the time scale for pattern formation. In this work, the shear state of an isolated granular gas will be analyzed. This is a two-band shear state with a steady density profile and an average temperature that decays in time with a Haff like law, but controlled by the viscosity of the gas. Hydrodynamics predicts that this state can only exist if the size of the system is larger than the critical size for the stability of the homogeneous cooling state, and expressions for the hydrodynamic fields in the limit of not too large inhomogeneities can be obtained. The theoretical predictions are compared with computer simulation results of a system of inelastic hard disks for several values of the coefficient of restitution, well beyond the quasi-elastic limit. It will be shown that the shear state is indeed exhibited by the system if its size is larger, but not much larger, than the critical size. The behaviour of the system and the way in which it deviates from the shear state as its size is increased will also be discussed.
KeywordsEuropean Physical Journal Special Topic System Size Critical Size Transverse Velocity Fourier Component
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