Spatial Correlations in Compressible Granular Flows

TL;DR

This paper extends fluctuating hydrodynamics to compressible granular flows, revealing unique long-range correlation behaviors and validating results with molecular dynamics simulations.

Contribution

It introduces a theoretical framework for compressible granular flows, including density and longitudinal velocity fluctuations, and compares predictions with simulations.

Findings

Density fluctuation structure factor peaks at finite wavenumber

Correlation length grows over time

Theory matches molecular dynamics simulations

Abstract

For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including longitudinal velocity and density fluctuations, and yields qualitatively different results for long range correlations. The structure factor of density fluctuations shows a maximum at finite wavenumber, shifting in time to smaller wavenumbers and corresponding to a growing correlation length. It agrees well with two-dimensional molecular dynamics simulations.