Rayleigh-Benard convection in a hard disk system

TL;DR

This study investigates Rayleigh-Benard convection in a hard disk system under thermal gradients and gravity, revealing scaling behaviors and conditions for local equilibrium, with implications for hydrodynamic modeling.

Contribution

It demonstrates the scaling of hydrodynamic fields with thermal gradient and shows local equilibrium holds only when mechanical and thermodynamic pressures differ.

Findings

Hydrodynamic fields scale with the thermal gradient.

Local equilibrium is violated when mechanical and thermodynamic pressures are equal.

Bulk viscosity depends on the mechanical pressure for best data fit.

Abstract

We do a generic study of the behavior of a hard disk system under the action of a thermal gradient in presence of an uniform gravity field. We observe the conduction-convection transition and measure the main system observables and fields as the thermal current, global pressure, velocity field, temperature field,... We can highlight two of the main results of this overall work: (1) for large enough thermal gradients and a given gravity, we show that the hydrodynamic fields (density, temperature and velocity) have a natural scaling form with the gradient. And (2) we show that local equilibrium holds if the mechanical pressure and the thermodynamic one are not equal, that is, the Stoke's assumption does not hold in this case. Moreover we observe that the best fit to the data is obtained when the bulk viscosity depends on the mechanical pressure.