Hydrodynamic Modes for Granular Gases

TL;DR

This paper analyzes the hydrodynamic modes of granular gases by calculating eigenfunctions and eigenvalues of the linearized Boltzmann equation, confirming the dominance of hydrodynamic behavior at long times and wavelengths.

Contribution

It provides explicit calculations of hydrodynamic modes and transport coefficients for inelastic hard spheres and disks, validating the hydrodynamic description for granular gases.

Findings

Transport coefficients agree with Chapman-Enskog results.

Hydrodynamic modes dominate at long times and wavelengths.

A bounded continuum ensures hydrodynamic behavior persists.

Abstract

The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport coefficients are identified and found to agree with those from the Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and long wavelengths is studied via an exactly solvable kinetic model. A collisional continuum is bounded away from the hydrodynamic spectrum, assuring a hydrodynamic description at long times. The bound is closely related to the power law decay of the velocity distribution in the reference homogeneous cooling state.