Thermally driven fluid convection in the incompressible limit regime

TL;DR

This paper analyzes the behavior of a heat-conducting, viscous fluid under thermal and gravitational influences in a low Mach and Froude number regime, identifying the limiting system as the Mach and Froude numbers approach zero.

Contribution

It derives the limit system for a compressible, heat-conducting fluid with inhomogeneous boundary temperature and external gravity in the low Mach/Froude number regime, including ill-prepared initial data.

Findings

Identified the limit system for the scaled Navier--Stokes--Fourier equations.

Showed the effects of boundary temperature distribution and gravity in the low Mach/Froude limit.

Analyzed the impact of acoustic wave reflection due to boundary conditions.

Abstract

We consider a scaled Navier--Stokes--Fourier system describing the motion of a compressible, heat-conducting, viscous fluid driven by inhomogeneous boundary temperature distribution together with the gravitational force of a massive object placed outside the fluid. We identify the limit system in the low Mach/low Froude number regime for the ill prepared initial data. The fluid is confined to a bounded cavity with acoustically hard boundary enhancing reflection of acoustic waves.