On singular limits arising in the scale analysis of stratified fluid flows

Abstract

We study the low Mach low Freude numbers limit in the compressible Navier–Stokes equations and the transport equation for evolution of an entropy variable — the potential temperature [Formula: see text]. We consider the case of well-prepared initial data on “flat” torus and Reynolds number tending to infinity, and the case of ill-prepared data on an infinite slab. In both cases, we show that the weak solutions to the primitive system converge to the solution to the anelastic Navier–Stokes system and the transport equation for the second-order variation of [Formula: see text].