Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

TL;DR

This paper performs a linear stability analysis of a confined quasi-two-dimensional granular gas model using inelastic Enskog kinetic equations, confirming the homogeneous steady state is stable for long wavelength disturbances at moderate densities.

Contribution

It introduces a stability analysis based on the inelastic Enskog kinetic equation for confined granular gases, extending previous dilute or quasielastic studies.

Findings

Homogeneous steady state is linearly stable for long wavelength excitations.

Stability analysis incorporates nonlinear dependence of transport coefficients and cooling rate.

Results apply to moderate densities, not just dilute systems.

Abstract

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.