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

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.