Granular Turbulence In Two Dimensions: Microscale Reynolds Number And Final Condensed States

Granular gases from the viewpoint of "two-dimensional turbulence" are investigated. In the quasi-elastic and thermodynamic limit, we obtained clear evidence for an enstrophy (square of vorticity) cascade and -3 exponent in the Kraichnan-Leith-Bachelor energy spectrum by performing large-scale (N similar to 16.8 million number of disks) event-driven molecular dynamics simulations. In these calculations, the enstrophy dissipation rate showed a strong relationship with the evolution of the exponent in the energy spectrum. The growth of the Reynolds number based on the microscale confirmed that the enstrophy cascade regime was that of fully developed turbulence. Moreover, a condensed state resembling Bose-Einstein condensation in decaying two-dimensional Navier-Stokes turbulence also appeared as the final attractor of the evolving granular gas in the long time limit.