Velocity Statistics in the Two-Dimensional Granular Turbulence

TL;DR

This study investigates the statistical properties of a large-scale two-dimensional granular system, revealing behaviors analogous to fluid turbulence, including enstrophy cascade, vortex formation, and clustering consistent with established turbulence theories.

Contribution

It provides the first large-scale simulation evidence of turbulence-like cascades and vortex dynamics in granular systems, bridging granular physics and fluid turbulence theories.

Findings

Energy spectra align with Kraichnan-Batchelor theory.

Squared two-particle separation follows Richardson law.

Distinct stages: homogeneous, shearing, clustering, final state.

Abstract

We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that 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.