Consequences of Symmetries on the Analysis and Construction of Turbulence Models

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, $\dots$), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.