On the incompressible limit of a strongly stratified heat conducting fluid

TL;DR

This paper investigates the behavior of a compressible, heat-conducting fluid under strong stratification, showing that in a certain asymptotic limit, the fluid dynamics simplify to Majda's layered flow model.

Contribution

It establishes the incompressible limit of a strongly stratified heat-conducting fluid, connecting it to Majda's layered flow model in a rigorous asymptotic framework.

Findings

Limit problem identified as Majda's layered flow model

Asymptotic analysis of Mach and Froude numbers

Validation of layered flow approximation in strong stratification

Abstract

A compressible, viscous and heat conducting fluid is confined between two parallel plates maintained at a constant temperature and subject to a strong stratification due to the gravitational force. We consider the asymptotic limit, where the Mach number and the Froude number are of the same order proportional to a small parameter. We show the limit problem can be identified with Majda's model of layered ``stack-of-pancake'' flow.