Nonlinear bounded convection and a phase separation instability in a dilute granular gas

A weakly nonlinear analysis using Stuart-Landau equation has been carried out to understand the onset of buoyancy-induced convection and a phase-separation instability of a dilute granular gas in a bounded domain. Previous linear stability analysis of the same base state showed that the conduction state is unstable for a range of Froude number and heat-loss parameter. A new instability mode has been found at very small values of the heat loss parameter, the origin of which is shown to be connected to the classical Rayleigh-Benard instability. The bifucation diagrams and the supercritical and subcritical nonlinear patterns with respect to inelasticity and Froude number will be discussed.