
As we discussed past week, at the moment the method is able to reproduce all the Reynolds tensor where %$ \lambda_i  2 \max{\lambda_i} > 0 $%.This conditions is spotted in the picture though a Lumley triangle. The dots are the result of a DNS channel flow (Kim et alt. 1999). We can suddenly see that me majority part of a real turbulence cannot be captured by the DFSEM. Is this a limit? Is this not a limit?
%BEGINLATEX{label="eq:Bousinnesq tensor"}%
\begin{equation*}
\tau_{ij}=\overline{\rho}\overline{u_{i}'u_{j}'}=\mu_{t}\left(\cfrac{\partial\overline{u}_{i}}{\partial x_{j}}+\frac{\partial\overline{u}_{j}}{\partial x_{i}}\right)\cfrac{2}{3}\rho k\delta_{ij}
\end{equation*}
%ENDLATEX%
The Bousinneq tensor, used in all 2 equations models, is highly isotropic (because of the second term in equation %reflatex{eq:Bousinnesq tensor}%. Their results are usually contained in the part of the Lumley triangle which we are able to reproduce then. Considering that, in a general simulation, there will be available only the RANS results, at the moment the method seems quite appropiate.