On a singular limit for stratified compressible fluids

TL;DR

This paper investigates the behavior of stratified compressible fluids in a low Mach number and strong stratification regime, deriving the anelastic Euler system as the singular limit for well-prepared initial data.

Contribution

It establishes the convergence of the compressible Euler system to the anelastic system in the low Mach and stratification limit, including dissipative measure-valued solutions.

Findings

Derivation of the anelastic Euler system as the singular limit.

Applicability to a broad class of dissipative measure-valued solutions.

Discussion of applications to driven shallow water equations.

Abstract

We consider a singular limit problem for the complete compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem - the anelastic Euler system - in the case of well prepared initial data. The result holds in the large class of the dissipative measure-valued solutions of the primitive system. Applications are discussed to the driven shallow water equations.