The Reynolds-Averaged Navier-Stokes (RANS) are a form of averaging of the Navier-Stokes Equations based on the Reynolds decomposition. This allows the treatment of perhaps the most controversial aspect of CFD: turbulence. The RANS approach is the foundation which the most used turbulence models rely on.

## Reynolds decomposition

The so-called Reynolds decomposition is based on the decomposition of instant values of velocity in the Navier-Stokes Equations into an average value ($\overline{U}$) and fluctuations ($u’$), so:

$U = \overline{U} + u’$

**[WORK IN PROGRESS]**

The snapshots below were all obtained from different RANS models: