Velocity statistics in two-dimensional granular turbulence

We studied the macroscopic statistical properties on the freely evolving quasielastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found it to be remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbulence. There are four typical stages in the freely evolving inelastic hard disk system, which are homogeneous, shearing (vortex), clustering, and final state. In the shearing stage, the self-organized macroscopic coherent vortices become dominant. In the clustering stage, the energy spectra are close to the expectation of Kraichnan-Batchelor theory and the squared two-particle separation strictly obeys Richardson law.