A better approach to assess mean flow stability in turbulence

There is a long history dating back to the 1950s of examining the stability of the turbulent mean profile in shear flows. Originally this was to explore the existence of a possible selection mechanism for the particular form of the mean flow and, latterly, has been used to help rationalise observed large scale structures seen in the turbulence. The stability `analysis’ usually applied consists simply of studying the spectral properties of the Orr-Sommerfeld equation built around the turbulent mean. We will discuss how to extend this naive approach to the next level of sophistication.