  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.
