Dear friends

I don't have much background in turbulence but I was thinking about a naive question about this subject.

It is known that according to the fluid velocity increases the inertial forces become more pronounced than the viscous forces (it's the assumption behind the definition of the Reynold's number). It is also known that in large eddy simulation (LES) the Navier Stokes equations are solved for the solvable scales and the fine scales are modeled by the addition of some kind of filter (the easiest and more straightforward way to filter the Navier Stokes equation, in a discrete scheme, is accomplished by the computational grid itself and this approach is known as SGS or SubGrid Scale). Furthermore, In the filtered form the Navier Stokes is almost the same that in the non filtered form and the differences appear only in the term related with the stresses in the fluid flow. In LES computations, this fact is frequently used to model the effect of turbulence by computing and adding a modeled "eddy viscosity" (this very simple, and less accurate, approach is used in the classical Smagorinsky's turbulence model).

Note that we have assumed by the Reynolds number definition that the viscous forces vanish in high speed flows but, even so, we are dealing with viscous terms to model a turbulence effect that, strictly speaking, is based on highly speed flows. It sounds strange for me and this is my naive thought (high speed flows modeled by viscous terms)... Where am I thinking wrong (or not)?!

Regards

Renato.

Inorder to understand the concept of eddy viscosity applied to high Re flows, you need to understand the concept of energy cascade proposed by Kolmogorv. Any standard book on turbulence will explain this.