Introduction to turbulence/Turbulence kinetic energy

From CFD-Wiki

It is clear from the previous chapter that the straightforward application of ideas that worked well for viscous stresses do not work too well for turbulence Reynolds stresses. Moreover, even the attempt to directly derive equations for the Reynolds stresses using the Navier-Stokes equations as a starting point has left us with far more equations than unknowns. Unfortunately this means that the turbulence problem for engineers is not going to have a simple solution: we simply cannot produce a set of reasonably universal equations. Obviously we are going to have to study the turbulence fluctuations in more detail and learn how they get their energy (usually from the mean flow somehow), and what they ultimately do with it. Our hope is that by understanding more about turbulence itself, we will gain insight into how we might make closure approximations that will work, at least sometimes. Hopefully, we will also gain an understanding of when and why they will not work.