Scale interactions in compressible rotating fluids

TL;DR

This paper investigates the behavior of a rotating, compressible viscous fluid under a specific singular limit, revealing that it converges to a purely horizontal, incompressible, inviscid flow described by an Euler-like system.

Contribution

It rigorously derives the limit equations for a rotating compressible Navier-Stokes system under simultaneous Mach and Rossby number scaling, with infinite Reynolds number, in a slab geometry.

Findings

Limit behavior is a purely horizontal, incompressible, inviscid flow.

The evolution is governed by an Euler-like system.

The analysis applies to fluids confined between parallel planes.

Abstract

We study a triple singular limit for the scaled barotropic Navier-Stokes system modeling the motion of a rotating, compressible, and viscous fluid, where the Mach and Rossby numbers are proportional to a small parameter, while the Reynolds number becomes infinite. If the fluid is confined to an infinite slab bounded above and below by two parallel planes, the limit behavior is identified as a purely horizontal motion of an incompressible inviscid fluid, the evolution of which is described by an analogue of the Euler system.