A singular limit for compressible rotating fluids

TL;DR

This paper investigates the behavior of rotating compressible fluids as key physical parameters approach zero, deriving a simplified 2-D Navier-Stokes model that includes effects of compressibility.

Contribution

It identifies the singular limit of the Navier-Stokes system for rotating compressible fluids as both Rossby and Mach numbers tend to zero, resulting in a modified 2-D model.

Findings

Derivation of the 2-D Navier-Stokes limit system with compressibility effects.

Analysis of the simultaneous zero limit of Rossby and Mach numbers.

Extension of understanding of fluid behavior in geophysical flows.

Abstract

We consider a singular limit problem for the Navier-Stokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the ``horizontal'' variables containing an extra term that accounts for compressibility in the original system.