The importance of turbulent equilibrium for Reynolds-stress modeling

Turbulence equilibrium state is analyzed for the modeled Reynolds-stress transport equation, assuming most general formulation of pressure–strain correlation. In a two-dimensional mean flow at high-Reynolds number, an algebraic equation system obtained, providing anisotropies as functions model coefficients. Conversely, equations provide calibration conditions coefficients to predict specified anisotropies. The predicted von-Kármán constant depends on and, hence, Identical can be obtained with different sets values invariants anisotropy tensor achieved, despite differing components. Numerical simulations Speziale–Sarkar–Gatski (SSG) model, using coefficients, confirm results theoretical analysis. They show that value Reynolds-shear stress determines skin friction boundary layer well spreading rate plane mixing layer. However, are required achieving good agreement experimental data both flows. Therefore, improvement turbulence models, set probably needs adapted local type flow. classification supposed suitable machine learning methods.