The paper discusses the way a simplified Langevin PDF approach models the turbulence transport. 
The authors show how in a weakly inhomogeneous turbulence regime, the Eulerian PDF of the simplified Langevin model expends at the first order and allows to recover a $k-\varepsilon$ like system. 

Numerical experiments complete this assert and are compared with the analytical self-similar compactly-supported Barenblatt solution to the k-epsilon system.  

Eulerian Monte Carlo simulation are used to study second and third order moments. 

For comparison, a finite volume method is also used, on the reduced-dimension PDF equation.