Statistically invariant eddy viscosity models

We presently generalize existing two-equation RANS models by using recent advances in our understanding of the Lie-symmetries governing turbulence. The motivation for this and the necessary steps are laid out using the conventional terminology of turbulence modeling, without requiring deep knowledge about the mathematical concept of symmetries. For illustration purposes, these steps are applied to the standard k-epsilon model and the k-omega model.The so modified k-epsilon model is applied to a wide range of canonical flows. For all of them, it is shown to match or even improve the performance of its classical counterpart and is, thus, shown to be more general than the original k-epsilon model