Thermodynamic inadmissibility of the incompressible hydrodynamics description of turbulent stratified fluid flows at low Mach numbers

TL;DR

This paper demonstrates that the common incompressible Navier-Stokes model for stratified turbulent flows at low Mach numbers is thermodynamically inadmissible when diabatic effects are significant, indicating a need for revised modeling approaches.

Contribution

It provides a first-principles thermodynamic critique of the incompressible assumption in stratified turbulence, highlighting the coupling of dynamics and thermodynamics.

Findings

Incompressible assumption invalidates when diabatic effects are present.

Thermodynamics and fluid dynamics are strongly coupled in stratified turbulence.

Revisiting physical models for stratified turbulence is necessary.

Abstract

The incompressible Navier-Stokes equations currently represent the primary model for describing stratified turbulent fluid flows at low Mach number. The validity of the incompressible assumption, however, has so far only been rigorously established for adiabatic motions. Here, we show from first principl es that the use of available energetics and thermodynamics considerations applied to a turbulent mixing event associated with stratified shear flow instability r efutes the widespread idea that the incompressible assumption is also valid when diabatic irreversible effects are important. The main consequence is that dynamics and thermodynamics are strongly coupled in stratified turbulence. This departs strongly from the currently accepted wisdom, and calls for a complete revisiting of the physical processes governing stratified turbulence at low Mach numbers.