Mesoscopic Theory of Granular Fluids

TL;DR

This paper develops a mesoscopic fluctuating hydrodynamics framework to describe long-range spatial correlations in freely evolving inelastic granular fluids, with results matching simulations in 2D.

Contribution

It introduces a theoretical approach for analyzing spatial correlations in granular fluids using fluctuating hydrodynamics, emphasizing the incompressible limit.

Findings

Velocity correlations decay as r^{-d} in the incompressible limit

The theory agrees with 2D simulations up to 50-100 collisions per particle

Incompressibility breaks down at large distances in the elastic limit

Abstract

Using fluctuating hydrodynamics we describe the slow build-up of long range spatial correlations in a freely evolving fluid of inelastic hard spheres. In the incompressible limit, the behavior of spatial velocity correlations (including $r^{-d}$-behavior) is governed by vorticity fluctuations only and agrees well with two-dimensional simulations up to 50 to 100 collisions per particle. The incompressibility assumption breaks down beyond a distance that diverges in the elastic limit.