Reynolds Experiments on Flow Stability
 

Reynolds Paper
 

Sir George Stokes wrote in his review of Reynolds paper: "The author (Osborne Reynolds) says that as a result of this the equtions are true, and only true, as applied to fluid, in which the mean motion, excluding the heat motions, are steady."
Since the work of Reynolds, over hundred years ago, the onset of turbulence is related to the incompressible Navier-Stokes equations. It seems that already Osborne Reynolds realized that this assumption might not be correct.
Heisenberg wrote in the paper "The relevance of Sommerfelds work today" in 1969 in relation to the stability of laminar flow in fluids: "However, as far as I know, even today it is not known what is actually wrong in the work of Noether. "
The incompressible Navier-Stokes and the Reynolds equations are approximations to the full Navier-Stokes equations. In an icompressible flow the energy equation is only satisfied for a non vanishing Prandtl number, if temperature gradients can be excluded and the background flow is stationary. Similar remarks apply to the classical boundary layer theory of Prandtl, based on the incompressible Navier-Stokes equations.
I think the nature of the transition to turbulence in shear flows is related to the temperature in the transition layer. I am looking for experimental results which include temperature measurements to validate theoretical results.