Inherent thermal convection in a gas inside a box under a gravity field

Abstract

We theoretically prove the existence in granular fluids of a thermal convection that is inherent, in the sense that is always present and has no thermal gradient threshold (convection occurs for all finite values of the Rayleigh number). More specifically, we study a gas of inelastic smooth hard disks enclosed in a rectangular region under a constant gravity field. The vertical walls act as energy sinks (i.e., inelastic walls that are parallel to gravity) whereas the other two walls are perpendicular to gravity and act as energy sources. We show that this convection is due to the combined action of dissipative lateral walls and a volume force (in this case, gravitation). Hence, we call it \textit{dissipative lateral walls convection}, DLWC. Our theory, that describes also the limit case of elastic collisions, shows that inelastic particle collisions enhance the DLWC. We perform our study via numerical solutions (volume element method) of the corresponding hydrodynamic equations, in an extended Boussinesq approximation. We show our theory describes the essentials of the results for similar (but more complex) laboratory experiments.