Thermal convection and the Boussinesq approximation for ideal gases in the light of kinetic theory
Phys. Rev. Fluids 10, 073401 – Published 15 July, 2025
DOI: https://doi.org/10.1103/474m-y29g
Abstract
A systematic asymptotic analysis of the Boltzmann equation for monatomic ideal gases is carried out under the conditions that the mean free path of gas molecules and the external force are both small, and the results are compared with the Boussinesq approximation of the conventional fluid dynamics. Under a suitable scaling that recovers the finite Rayleigh number, a fluid-dynamic-type set of equations similar to the one for the Boussinesq approximation is obtained. However, the obtained energy equation is not the same as that in the usual Boussinesq approximation. The difference implies that the usual Boussinesq approximation fails to correctly take account of the work done by the pressure. This difference affects the flow field as well through the buoyancy effect. Numerical simulations are carried out to demonstrate the quantitative impact of the difference.
